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  • 1.
    Abazari, Tina
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Baghchesara, Sherwin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Predicting Stock Price Direction for Asian Small Cap Stocks with Machine Learning Methods2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Portfolio managers have a great interest in detecting high-performing stocks early on. Detecting outperforming stocks has for long been of interest from a research as well as financial point of view. Quantitative methods to predict stock movements have been widely studied in diverse contexts, where some present promising results. The quantitative algorithms for such prediction models can be, to name a few, support vector machines, tree-based methods, and regression models, where each one can carry different predictive power. Most previous research focuses on indices such as S&P 500 or large-cap stocks, while small- and micro-cap stocks have been examined to a lesser extent. These types of stocks also commonly share the characteristic of high volatility, with prospects that can be difficult to assess. This study examines to which extent widely studied quantitative methods such as random forest, support vector machine, and logistic regression can produce accurate predictions of stock price directions on a quarterly and yearly basis. The problem is modeled as a binary classification task, where the aim is to predict whether a stock achieves a return above or below a benchmark index. The focus lies on Asian small- and micro-cap stocks. The study concludes that the random forest method for a binary yearly prediction produces the highest accuracy of 69.64%, where all three models produced higher accuracy than a binary quarterly prediction. Although the statistical power of the models can be ruled adequate, more extensive studies are desirable to examine whether other models or variables can increase the prediction accuracy for small- and micro-cap stocks.

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  • 2.
    Abdullah Mohamad, Ormia
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Westin, Anna
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Pricing and Modeling Heavy Tailed Reinsurance Treaties - A Pricing Application to Risk XL Contracts2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    To estimate the risk of a loss occurring for insurance takers is a difficult task in the insurance industry. It is an even more difficult task to price the risk for reinsurance companies which insures the primary insurers. Insurance that is bought by an insurance company, the cedent, from another insurance company, the reinsurer, is called treaty reinsurance. This type of reinsurance is the main focus in this thesis. A very common risk to insure, is the risk of fire in municipal and commercial properties which is the risk that is priced in this thesis. This thesis evaluates Länsförsäkringar AB's current pricing model which calculates the risk premium for Risk XL contracts. The goal of this thesis is to find areas of improvement for tail risk pricing. The risk premium can be calculated commonly by using one of three different types of pricing models, experience rating, exposure rating and frequency-severity rating. This thesis focuses on frequency-severity pricing, which is a model that assumes independence between the frequency and the severity of losses, and therefore splits the two into separate models. This is a very common model used when pricing Risk XL contracts. The risk premium is calculated with the help of loss data from two insurance companies, from a Norwegian and a Finnish insurance company. The main focus of this thesis is to price the risk with the help of extreme value theory, mainly with the method of moments method to model the frequency of losses, and peaks over threshold model to model the severity of the losses. In order to model the estimated frequency of losses by using the method of moments method, two distributions are compared, the Poisson and the negative binomial distribution. There are different distributions that can be used to model the severity of losses. In order to evaluate which distribution is optimal to use, two different Goodness of Fit tests are applied, the Kolmogorov-Smirnov and the Anderson-Darling test. The Peaks over threshold model is a model that can be used with the Pareto distribution. With the help of the Hill estimator we are able to calculate a threshold $u$, which regulates the tail of the Pareto curve. To estimate the rest of the ingoing parameters in the generalized Pareto distribution, the maximum likelihood and the least squares method are used. Lastly, the bootstrap method is used to estimate the uncertainty in the price which was calculated with the help of the estimated parameters. From this, empirical percentiles are calculated and set as guidelines to where the risk premium should lie between, in order for both the data sets to be considered fairly priced.

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  • 3.
    Abrahamsson, Peter
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Ahlqvist, Niklas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Evaluation of Machine Learning Methods for Time Series Forecasting on E-commerce Data2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Within demand forecasting, and specifically within the field of e-commerce, the provided data often contains erratic behaviours which are difficult to explain. This induces contradictions to the common assumptions within classical approaches for time series analysis. Yet, classical and naive approaches are still commonly used. Machine learning could be used to alleviate such problems. This thesis evaluates four models together with Swedish fin-tech company QLIRO AB. More specifically, a MLR (Multiple Linear Regression) model, a classic Box-Jenkins model (SARIMAX), an XGBoost model, and a LSTM-network (Long Short-Term Memory). The provided data consists of aggregated total daily reservations by e-merchants within the Nordic market from 2014. Some data pre processing was required and a smoothed version of the data set was created for comparison. Each model was constructed according to their specific requirements but with similar feature engineering. Evaluation was then made on a monthly level with a forecast horizon of 30 days during 2021. The results shows that both the MLR and the XGBoost provides the most consistent results together with perks for being easy to use. After these two, the LSTM-network showed the best results for November and December on the original data set but worst overall. Yet it had good performance on the smoothed data set and was then comparable to the first two. The SARIMAX was the worst performing of all the models considered in this thesis and was not as easy to implement.

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  • 4.
    Agram, Nacira
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Hu, Yaozhong
    Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada..
    oksendal, Bernt
    Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway..
    Mean-field backward stochastic differential equations and applications2022In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 162, article id 105196Article in journal (Refereed)
    Abstract [en]

    In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.

  • 5.
    Aleksanyan, Hayk
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Sjölin, Per
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Applications of Fourier Analysis in Homogenization of the Dirichlet Problem: L-p Estimates2015In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 215, no 1, p. 65-87Article in journal (Refereed)
    Abstract [en]

    Let u(epsilon) be a solution to the system div(A(epsilon)(x)del u(epsilon)(x)) = 0 in D, u(epsilon)(x) = g(x, x/epsilon) on partial derivative D, where D subset of R-d (d >= 2), is a smooth uniformly convex domain, and g is 1-periodic in its second variable, and both A(epsilon) and g are sufficiently smooth. Our results in this paper are twofold. First we prove L-p convergence results for solutions of the above system and for the non-oscillating operator A(epsilon)(x) = A(x), with the following convergence rate for all 1 <= p < infinity parallel to u(epsilon) - u(0)parallel to (LP(D)) <= C-P {epsilon(1/2p), d = 2, (epsilon vertical bar ln epsilon vertical bar)(1/p), d = 3, epsilon(1/p), d >= 4, which we prove is (generically) sharp for d >= 4. Here u(0) is the solution to the averaging problem. Second, combining our method with the recent results due to Kenig, Lin and Shen (Commun Pure Appl Math 67(8): 1219-1262, 2014), we prove (for certain class of operators and when d >= 3) ||u(epsilon) - u(0)||(Lp(D)) <= C-p[epsilon(ln(1/epsilon))(2)](1/p) for both the oscillating operator and boundary data. For this case, we take A(epsilon) = A(x/epsilon), where A is 1-periodic as well. Some further applications of the method to the homogenization of the Neumann problem with oscillating boundary data are also considered.

  • 6. Almquist, Martin
    et al.
    Karasalo, Ilkka
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    Mattsson, Ken
    Atmospheric Sound Propagation Over Large-Scale Irregular Terrain2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, no 2, p. 369-397Article in journal (Refereed)
    Abstract [en]

    A benchmark problem on atmospheric sound propagation over irregular terrain has been solved using a stable fourth-order accurate finite difference approximation of a high-fidelity acoustic model. A comparison with the parabolic equation method and ray tracing methods is made. The results show that ray tracing methods can potentially be unreliable in the presence of irregular terrain.

  • 7.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Harmonic Lyapunov functions in the analysis of periodically switched systems2006In: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, p. 2759-2764Conference paper (Refereed)
    Abstract [en]

    The dynamic phasor model of a time-periodic system is used to derive a stability test involving a harmonic Lyapunov function. This reveals a new interpretation of the harmonic Lyapunov function with an appealing time-domain representation. Most importantly, it indicates that the ideas behind the harmonic Lyapunov equation can be generalized to include cyclic switching systems that have different pulse form in each period.

  • 8.
    Altafi, Nasrin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Jordan types with small parts for Artinian Gorenstein algebras of codimension three2022In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 646, p. 54-83Article in journal (Refereed)
    Abstract [en]

    We study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We show that there is a 1-1 correspondence between rank matrices and Jordan degree types. For Artinian Gorenstein algebras with codimension three we classify all rank matrices that occur for linear forms with vanishing third power. As a consequence, we show for such algebras that the possible Jordan types with parts of length at most four are uniquely determined by at most three parameters.

  • 9.
    Alvehag, Karin
    et al.
    KTH, School of Electrical Engineering (EES), Electric Power Systems.
    Martin, Clyde
    Texas Tech University.
    The Feedback Control of Glucose: On the road to type II diabetes2006In: Proceedings of the 45th IEEE Conference on Decision & Control, 2006, p. 685-690Conference paper (Refereed)
    Abstract [en]

    This paper develops a mathematical model for the feedback control of glucose regulation in the healthy human being and is based on the work of Sorensen (1985). The proposed model serves as a starting point for modeling type H diabetes. Four agents - glucose and the three hormones insulin, glucagon, and incretins - are assumed to have an effect on glucose metabolism. By letting compartments represent anatomical organs, the model has a close resemblance to a real human body. Mass balance equations that account for blood flows, exchange between compartments, and metabolic sinks and sources are written, and these result in simultaneous differential equations that are solved numerically. The metabolic sinks and sources - removing or adding glucose, insulin, glucagon, and incretins - describe physiological processes in the body. These processes function as feedback control systems and have nonlinear behaviors. The results of simulations performed for three different clinical test types indicate that the model is successful in simulating intravenous glucose, oral glucose, and meals containing mainly carbohydrates.

  • 10.
    Andersson, Hannes
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Sjöberg, John
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Predicting the Impact of Supply Chain Disruptions Using Statistical Analysis and Machine Learning2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The dairy business is vulnerable to supply chain disruptions since large safety stocks to cover up losses are not always a viable option, therefore it is crucial to maintain a smooth supply chain to ensure stable delivery accuracies. Disruptions are unpredictable and hard to avoid in the supply chain, especially in cases where production errors cause lost production volume. This thesis proposes the use of machine learning and statistical modelling together with data from Arla to predict when a shortage will occur and its duration to allow proactive decision making to mitigate the consequences of the disruption. The aim of this thesis is to create one predictive model for delay and one for duration based on data from multiple products and explore how the features and methods used can capture the product specific characteristics in the data and thereupon improve the models. The model used for evaluating these factors was a random forest classifier, and permutation feature importance was used to determine the relevant features for the models. The issue of having imbalanced data was handled by first grouping the data and then applying the oversampling method SMOTE. The two models were trained on different datasets where the duration model was trained on all disruptions and the delay model was only trained on a subset were a shortage have occurred. One finding was that applying SMOTE yielded the best results. The best duration model had an accuracy of 62% with precision and recall of 79% and 76% respectively for the majority class, but very low for the other classes with a combined average of 21% and 24%. The most important feature for the duration was the the quotient describing the lost production. The best delay model had an accuracy of 62% with more accurate predictions over all classes and an average precision and recall of 59% and 57%. The most important feature for the delay was how often a product is produced.

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  • 11.
    Andersson, Joel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Strömberg, Jan-Olov
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the Theorem of Uniform Recovery of Random Sampling Matrices2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 3, p. 1700-1710Article in journal (Refereed)
    Abstract [en]

    We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.

  • 12.
    Andersson, Linnéa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Stochastic Lateral Transshipment within the Fast Fashion Industry2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In an industry with highly variable demand and a fickle customer demanding a fast changing supply, quickly responding to the customer becomes crucial for the fast fashion retailer. Using lateral transshipment, one is able to reorganize supply within an echelon of the supply chain to quickly respond to the forecasted demand by looking at shorter more accurate forecasts and act accordingly. Due to the uncertainty of demand there is the question of if introducing stochasticity into the optimization model can improve the outcome. In this thesis a case study is conducted together with H&M Group to solve the transshipment problem with a Two-Stage Recourse Problem with Sample Average Approximation (SAA). The problem was solved for four warehouses within the same geographical region, 18 325 variants, and 5 sample sets in the SAA. A variant is defined as a product of a specific colour and size. The model was compared to the wait and see solution (WS) as well as the solution given by the expected value problem (EV). The recourse problem resulted in the mean and median service level of each warehouse increasing, no matter if they ship more items than they receive, and the mean service level over all variants increasing. It was then shown that despite a small aggregate value of the stochastic solution (VSS) of approximately 3.7%, using a stochastic model led to a 1.3 percentage point (pp) larger increase of mean service level for the entire system, as well as a roughly 20pp increase of the median ”mean service level” for items across all warehouses. So, despite a small decrease in cost the result on the service level is a great benefit in a setting where service levels is of high importance.

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  • 13. Andersson, Ola
    et al.
    Argenton, Cedric
    Weibull, Jörgen W.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Robustness to strategic uncertainty2014In: Games and Economic Behavior, ISSN 0899-8256, E-ISSN 1090-2473, Vol. 85, no 1, p. 272-288Article in journal (Refereed)
    Abstract [en]

    We introduce a criterion for robustness to strategic uncertainty in games with continuum strategy sets. We model a player's uncertainty about another player's strategy as an atomless probability distribution over that player's strategy set. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others. When payoff functions are continuous we show that our criterion is a refinement of Nash equilibrium and we also give sufficient conditions for existence of a robust strategy profile. In addition, we apply the criterion to Bertrand games with convex costs, a class of games with discontinuous payoff functions and a continuum of Nash equilibria. We show that it then selects a unique Nash equilibrium, in agreement with some recent experimental findings.

  • 14.
    Andersson, Pelle
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Tensor rank and support rank in the context of algebraic complexity theory2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Starting with the work of Volker Strassen, algorithms for matrix multiplication have been developed which are time complexity-wise more efficient than the standard algorithm from the definition of multiplication. The general method of the developments has been viewing the bilinear mapping that matrix multiplication is as a three-dimensional tensor, where there is an exact correspondence between time complexity of the multiplication algorithm and tensor rank. The latter can be seen as a generalisation of matrix rank, being the minimum number of terms a tensor can be decomposed as. However, in contrast to matrix rank there is no general method of computing tensor ranks, with many values being unknown for important three-dimensional tensors. To further improve the theoretical bounds of the time complexity of matrix multiplication, support rank of tensors has been introduced, which is the lowest rank of tensors with the same support in some basis. The goal of this master's thesis has been to go through the history of faster matrix multiplication, as well as specifically examining the properties of support rank for general tensors. In regards to the latter, a complete classification of rank structures of support classes is made for the smallest non-degenerate tensor product space in three dimensions. From this, the size of a support can be seen affecting the pool of possible ranks within a support class. At the same time, there is in general no symmetry with regards to support size occurring in the rank structures of the support classes, despite there existing a symmetry and bijection between mirrored supports. Discussions about how to classify support rank structures for larger tensor product spaces are also included.

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  • 15.
    Anisi, David A.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Adaptive node distribution for on-line trajectory planning2006In: ICAS-Secretariat - 25th Congress of the International Council of the Aeronautical Sciences 2006, Curran Associates, Inc., 2006, p. 3150-3157Conference paper (Refereed)
    Abstract [en]

    Direct methods for trajectory optimization are traditionally based on a priori temporal dis- cretization and collocation methods. In this work, the problem of node distribution is for- mulated as an optimization problem, which is to be included in the underlying non-linear mathematical programming problem (NLP). The benefits of utilizing the suggested method for on-line trajectory optimization are illustrated by a missile guidance example.

  • 16.
    Anisi, David A.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ögren, Petter
    Department of Autonomous Systems Swedish Defence Research Agency.
    Robinson, John W. C.
    Department of Autonomous Systems Swedish Defence Research Agency.
    Safe receding horizon control of an aerial vehicle2006In: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, IEEE , 2006, p. 57-62Conference paper (Refereed)
    Abstract [en]

    This paper addresses the problem of designing a real time high performance controller and trajectory generator for air vehicles. The control objective is to use information about terrain and enemy threats to fly low and avoid radar exposure on the way to a given target. The proposed algorithm builds on the well known approach of Receding Horizon Control (RHC) combined with a terminal cost, calculated from a graph representation of the environment. Using a novel safety maneuver, and under an assumption on the maximal terrain inclination, we are able to prove safety as well as task completion. The safety maneuver is incorporated in the short term optimization, which is performed using Nonlinear Programming (NLP). Some key characteristics of the trajectory planner are highlighted through simulations.

  • 17. Apushkinskaya, D.
    et al.
    Petrosyan, A.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Nina Nikolaevna Uraltseva2022In: Notices of the American Mathematical Society, ISSN 0002-9920, E-ISSN 1088-9477, Vol. 69, no 03, p. 1-395Article in journal (Refereed)
  • 18.
    Armerin, Fredrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    An axiomatic approach to the valuation of cash flows2014In: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, Vol. 2014, no 1, p. 32-40Article in journal (Refereed)
    Abstract [en]

    We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options.

  • 19.
    Arthursson, Karl
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Using topology and signature methods to study spatiotemporal data with machine learning2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis explores a new way to analyze spatiotemporal data. By combining topology, the path signature and machine learning a robust model to analyze swarming behavior over time is created. Using persistent homology a representation of spatial data is obtained and the path signature gives us a representation for how this changes over time. This representation allows us to compare samples even if they have different amounts of time steps and different length of the sequence. It is also resistant to noise in the spatial representation. Using this data is then used to train a gaussian process regressor to extract parameters that govern the movement of swarms. Our analysis shows that the tested method is a good candidate for analyzing spatiotemporal data and that it warrants further studies.

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  • 20.
    Atli Thorsteinsson, Jakob
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Clustering and classification of prepaid mortgages2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis aims to cluster and classify mortgages issued by a financial institution. The aim is to apply machine learning techniques on historical data in order to discover a possible structure and predictability in prepaid mortgages. To discover the underlying structure of the data \textit{k}-means clustering on principal components is performed to cluster customers with mortgages.A logistic regression model is trained to predict how likely (future) customers with mortgages are to prepay their loans, hence moving them to another institution. The classification model is evaluated using confusion matrices for different levels of thresholds. The results show that based on historical data the model detects clusters which include a higher proportion of mortgages being prepaid. This indicating an underlying structure which can be used to determine a riskiness of leaving for customers within each cluster. The results from the logistic regression show a significant improvement in precision by using a high threshold in the classification.

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  • 21.
    Aurell, Alexander
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations2018In: Games, E-ISSN 2073-4336, Vol. 9, no 5Article in journal (Refereed)
    Abstract [en]

    In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum, non-cooperating, differential games where the players’ state dynamics solve backward stochastic differential equations (BSDE) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of playercosts, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

  • 22.
    Aurell, Alexander
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Topics in the mean-field type approach to pedestrian crowd modeling and conventions2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of five appended papers, primarily addressingtopics in pedestrian crowd modeling and the formation of conventions.The first paper generalizes a pedestrian crowd model for competingsubcrowds to include nonlocal interactions and an arbitrary (butfinite) number of subcrowds. Each pedestrian is granted a ’personalspace’ and is effected by the presence of other pedestrians within it.The interaction strength may depend on subcrowd affinity. The paperinvestigates the mean-field type game between subcrowds and derivesconditions for the reduction of the game to an optimization problem.The second paper suggest a model for pedestrians with a predeterminedtarget they have to reach. The fixed and non-negotiablefinal target leads us to formulate a model with backward stochasticdifferential equations of mean-field type. Equilibrium in the game betweenthe tagged pedestrians and a surrounding crowd is characterizedwith the stochastic maximum principle. The model is illustrated by anumber of numerical examples.The third paper introduces sticky reflected stochastic differentialequations with boundary diffusion as a means to include walls andobstacles in the mean-field approach to pedestrian crowd modeling.The proposed dynamics allow the pedestrians to move and interactwhile spending time on the boundary. The model only admits a weaksolution, leading to the formulation of a weak optimal control problem.The fourth paper treats two-player finite-horizon mean-field typegames between players whose state trajectories are given by backwardstochastic differential equations of mean-field type. The paper validatesthe stochastic maximum principle for such games. Numericalexperiments illustrate equilibrium behavior and the price of anarchy.The fifth paper treats the formation of conventions in a large populationof agents that repeatedly play a finite two-player game. Theplayers access a history of previously used action profiles and form beliefson how the opposing player will act. A dynamical model wheremore recent interactions are considered to be more important in thebelief-forming process is proposed. Convergence of the history to acollection of minimal CURB blocks and, for a certain class of games,to Nash equilibria is proven.

  • 23.
    Aurell, Alexander
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Dinetan, Lee
    Karreskog, Gustav
    Stochastic stability of mixed equilibriaManuscript (preprint) (Other academic)
  • 24.
    Axén, Magnus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Imitation Learning on Branching Strategies for Branch and Bound Problems2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    A new branch of machine and deep learning models has evolved in constrained optimization, specifically in mixed integer programming problems (MIP). These models draw inspiration from earlier solver methods, primarily the heuristic, branch and bound. While utilizing the branch and bound framework, machine and deep learning models enhance either the computational efficiency or performance of the model. This thesis examines how imitating different variable selection strategies of classical MIP solvers behave on a state-of-the-art deep learning model.

    A recently developed deep learning algorithm is used in this thesis, which represents the branch and bound state as a bipartite graph. This graph serves as the input to a graph network model, which determines the variable in the MIP on which branching occurs. This thesis compares how imitating different classical branching strategies behaves on different algorithm outputs and, most importantly, time span. More specifically, this thesis conducts an empirical study on a MIP known as the facility location problem (FLP) and compares the different methods for imitation.

    This thesis shows that the deep learning algorithm can outperform the classical methods in terms of time span. More specifically, imitating the branching strategies resulting in small branch and bound trees give rise to a more rapid performance in finding the global optimum. Lastly, it is shown that a smaller embedding size in the network model is preferred for these instances when looking at the trade-off between variable selection and time cost.

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  • 25.
    Backe, Hannes
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Rydberg, David
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Statistical Modelling of Price Difference Durations Between Limit Order Books: Applications in Smart Order Routing2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The modern electronic financial market is composed of a large amount of actors. With the surge in algorithmic trading some of these actors collectively behave in increasingly complex ways. Historically, academic research related to financial markets has been focused on areas such as asset pricing, portfolio management and financial econometrics. However, the fragmentation of the financial market has given rise to a different set of problems, namely the order allocation problem, as well as smart order routers as a tool to comply with these. In this thesis we consider price discrepancies between order books, trading the same instruments, as a proxy for order routing opportunities. A survival analysis framework for these price differences is developed. Specifically, we consider the two widely used Kaplan-Meier and Cox Proportional Hazards models, as well as the somewhat less known Random Survival Forest model, in order to investigate whether such a framework is effective for predicting the survival times of price differences. The results show that the survival models outperform random models and fixed routing decisions significantly. Thus suggesting that such models could beneficially be incorporated into existing SOR environments. Furthermore, the implementation of order book parameters as covariates in the CPH and RSF models add additional performance.

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  • 26.
    Barreira, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Enhancing Neural Network Accuracy on Long-Tailed Datasets through Curriculum Learning and Data Sorting2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this paper, a study is conducted to investigate the use of Curriculum Learning as an approach to address accuracy issues in a neural network caused by training on a Long-Tailed dataset. The thesis problem is presented by a Swedish e-commerce company. Currently, they are using a neural network that has been modified by them using a CORAL framework. This adaptation means that instead of having a classic binary regression model, it is an ordinal regression model. The data used for training the model has a Long-Tail distribution, which leads to inaccuracies when predicting a price distribution for items that are part of the tail-end of the data. The current method applied to remedy this problem is Re-balancing in the form of down-sampling and up-sampling. A linear training scheme is introduced, increasing in increments of $10\%$ while applying Curriculum Learning. As a method for sorting the data in an appropriate way, inspiration is drawn from Knowledge Distillation, specifically the Teacher-Student model approach. The teacher models are trained as specialists on three different subsets, and furthermore, those models are used as a basis for sorting the data before training the student model. During the training of the student model, the Curriculum Learning approach is used. The results show that for Imbalance Ratio, Kullback-Liebler divergence, Class Balance, and the Gini Coefficient, the data is clearly less Long-Tailed after dividing the data into subsets. With the correct settings before training, there is also an improvement in the training speed of the student model compared to the base model. The accuracy for both the student model and the base model is comparable. There is a slight advantage for the base model when predicting items in the head part of the data, while the student model shows improvements for items that are between the head and the tail.

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  • 27.
    Barry, Viktor
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Stenfelt, Carl
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Applying the Shadow Rating Approach: A Practical Review2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The combination of regulatory pressure and rare but impactful defaults together comprise the domain of low default portfolios, which is a central and complex topic that lacks clear industry standards. A novel approach that utilizes external data to create a Shadow Rating model has been proposed by Ulrich Erlenmaier. It addresses the lack of data by estimating a probability of default curve from an external rating scale and subsequently training a statistical model to estimate the credit rating of obligors.

    The thesis intends to first explore the capabilities of the Cohort model and the Pluto and Tasche model to estimate the probability of default associated with banks and financial institutions through the use of external data. Secondly, the thesis will implement a multinomial logistic regression model, an ordinal logistic regression model, Classification and Regression Trees, and a Random Forest model. Subsequently, their performance to correctly estimate the credit rating of companies in a portfolio of banks and financial institutions using financial data is evaluated. Results suggest that the Cohort model is superior in modelling the underlying data, given a Gini coefficient of 0.730 for the base case, as opposed to Pluto and Tasche's 0.260. Moreover, the Random Forest model displays marginally higher performance across all metrics (such as an accuracy of 57%, a mean absolute error of 0.67 and a multiclass receiver operating characteristic of 0.83). However, given a lower degree of interpretability, the more simplistic ordinal logistic regression model (50%, 0.80 and 0.81, respectively) can be preferred due to its clear interpretability and explainability.

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  • 28.
    Barysheva, Anna
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Computer Vision in Fitness: Exercise Recognition and Repetition Counting2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Motion classification and action localization have rapidly become essential tasks in computer vision and video analytics. In particular, Human Action Recognition (HAR), which has important applications in clinical assessments, activity monitoring, and sports performance evaluation, has drawn a lot of attention in research communities. Nevertheless, the high-dimensional and time-continuous nature of motion data creates non-trivial challenges in action detection and action recognition.

    In this degree project, on a set of recorded unannotated mixed workouts, we test and evaluate unsupervised and semi-supervised machine learning models to identify the correct location, i.e., a timestamp, of various exercises in videos and to study different approaches in clustering detected actions. This is done by modelling the data via the two-step clustering pipeline using the Bag-of-Visual-Words (BoVW) approach. Moreover, the concept of repetition counting is under consideration as a parallel task.

    We find that clustering alone tends to produce cluster solutions with a mixture of exercises and is not sufficient to solve the exercise recognition problem. Instead, we use clustering as an initial step to aggregate similar exercises. This allows us to effectively find many repetitions of similar exercises for their further annotation. When combined with a subsequent Support Vector Machine (SVM) classifier, the BoVW concept proved itself, achieving an accuracy score of 95.5% on the labelled subset. Much attention has also been paid to various methods of dimensionality reduction and benchmarking their ability to encode the original data into a lower-dimensional latent space.

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  • 29.
    Basilio Kuosmanen, Seuri
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Symmetry in a free boundary problem2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    We consider a variational formulation of a Bernoulli-type free boundary problem for the Laplacian operator with discontinuous boundary data. We show the existence of a weak solution to the problem. Moreover, we show that the solution has symmetry properties inherited by symmetric data. These results are achieved through the use of comparison arguments, the celebrated method of moving planes, and several elaborated techniques from existing literature.

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  • 30. Bauso, Dario
    et al.
    Dia, Ben Mansour
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Tembine, Hamidou
    Tempone, Raul
    Mean-Field Games for Marriage2014In: PLOS ONE, E-ISSN 1932-6203, Vol. 9, no 5, p. e94933-Article in journal (Refereed)
    Abstract [en]

    This article examines mean-field games for marriage. The results support the argument that optimizing the long-term wellbeing through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.

  • 31.
    Becedas, Adrian
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Voronoi Cells of Varieties with respect to Wasserstein Distances2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Voronoi diagrams are partitions of a metric space into Voronoi cells according to distance from points on some set w.r.t. some distance. In this thesis we examine Voronoi diagrams of manifolds and varieties w.r.t. the Wasserstein distance from probability theory. We give some upper and lower bounds on the dimension of Voronoi cells based on the geometry of the manifolds and Wasserstein distance balls. We provide an upper bound on the number of full-dimensional Voronoi cells of algebraic varieties and show examples of the bound being tight.

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  • 32.
    Bellander, Victor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sequential Machine Learning in Material Science2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    This report evaluates the possibility of using sequential learning in a material development setting to help predict material properties and speed up the development of new materials. To do this a Random forest model was built incorporating carefully calibrated prediction uncertainty estimates. The idea behind the model is to use the few data points available in this field and leverage that data to build a better representation of the input-output space as each experiment is performed. Having both predictions and uncertainties to evaluate, several different strategies were developed to investigate performance. Promising results regarding feasibility and potential cost-cutting were found using these strategies. It was found that within a specific performance region of the output space, the mean difference in alloying component price between the cheapest and most expensive material could be as high as 100 %. Also, the model performed fast extrapolation to previously unknown output regions, meaning new, differently performing materials could be found even with very poor initial data.

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  • 33.
    Benckert, Alexandra
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Loft, My
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Modelling Non-Maturing Deposits: Examining the Impact of Repo Rates and Volume Dynamics on Valuation Using Regression, Time Series Analysis, and Vasicek Methods2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis focuses on modelling non-maturing deposits (NMD) and has been written in collaboration with Svenska Handelsbanken. The methodology includes regression analysis and time series analysis, with the Repo rate serving as an exogenous variable in both models. A Vasicek model is employed to generate future Repo rates, which are then used as inputs for forecasting the NMD volume. These simulated rates are then compared to forecasted Repo rates with discrete changes from an external source. The results are utilised to analyze how net interest income can vary in the case of constant volume and in the case of interest rate-dependent volume.

    Effective liquidity management is crucial for banks, and NMDs are an important source of funding. By using regression analysis and time series analysis, combined with the Repo rate as the exogenous variable, this thesis provides insights into the behaviour of NMD volumes, and how it is affected by the Repo rate. The models also enable the forecasting of future trends based on future Repo rates. Additionally, by using different data sets as input for future Repo rates, the behaviour of the model can be evaluated based on how well it coincides with reality. The results obtained from this analysis can also be used to compare the value and interest rate sensitivity of NMD products.

    In conclusion, this thesis provides an approach to modelling the NMD volumes using exogenous factors and demonstrates how this can affect the net interest income from deposit volumes.

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  • 34.
    Berg Wahlström, Max
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hagelberg, Anton
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Analysis and Use of Telemetry Data for Car Insurance Premiums2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Paydrive is a pioneer in the Swedish auto insurance market. Being able to influence your insurancepremium through your driving is a concept that is still in its early stages. Throughout this thesis,an attempt to consolidate the vast amounts of data gathered while driving with neural networkshas been made, together with comparisons to the currently existing generalized linear models. Inthe end, a full analysis of the data yielded four distinct groupings of customer behavior but becauseof how the data is structured the results from the modeling became sub-optimal. Insurance datais typically very skewed and zero-heavy due to the absence of accidents. The original researchquestion is whether it is possible to use two neural networks, calculating the probability of anaccident, r, and the size of a potential claim, s respectively. These two factors could be multipliedto determine a final insurance premium as c = r · s.

    Using statistical standards and tools such as the Gini-coefficient, R2 values, MSE, and MAE themodels were evaluated both individually and pairwise. However, previous research in the fieldshows there haven’t been big enough advancements in this area yet. This thesis comes to the sameconclusion that due to the volatile nature of neural networks and the skewness of the data, it isincredibly difficult to get good results. Future work in the field could result in fairer prices forcustomers on their insurance premiums.

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  • 35.
    Bergman, Anton
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Numerical simulations oflovastatin crystallization in aT-shaped 2D mixer2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The rise of battery driven technology and the strive towards circular economy calls for the indefinite recycling of metals used in batteries. To be able to study and optimize the processes used in recycling, mathematical models are required. One way of recycling metals is to leach them into an acid, this solution is then mixed with an anti-solvent to induce cryztallization of the metal. The resulting crystals can then be retrieved and further processed. This type of process is also used in the pharmaceutical industry to crystallize medicines. A mathematical model and a solver has been developed at KAIST (Korean Advanced Institute of Science and Technology) called multiphase particle-in-cell coupled with population balance equation (MP-PIC-PBE) that can model anti-solvent crystallization in pharmaceuticals. This paper provides a thorough description on the governing mathematical equations as well as the numerical framework used to solve them. A study of the discretization of the internal coordinates is performed to determine the appropriate discretization. Further the associated CFD-solver implemented in OpenFOAM is applied to simulate the mixing of a solution of lovastatin in methanol being mixed with pure water as an anti-solvent. The geometry is a 2 dimensional T-shaped mixer. For the simulation results presented here, the Reynolds number based on the injected solution is kept constant at 4000 while four different solution temperatures are considered. Finally, the paper concludes with a discussion of the model and solver, and some recommendations for future work are provided.

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  • 36.
    Bhardwaj, Lakshya
    et al.
    Mathematical Institute, University of Oxford, Andrew-Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK, Andrew-Wiles Building, Woodstock Road.
    Schäfer-Nameki, Sakura
    Mathematical Institute, University of Oxford, Andrew-Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK, Andrew-Wiles Building, Woodstock Road.
    Tiwari, Apoorv
    KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Unifying constructions of non-invertible symmetries2023In: SciPost Physics, E-ISSN 2542-4653, Vol. 15, no 3, article id 122Article in journal (Refereed)
    Abstract [en]

    In the past year several constructions of non-invertible symmetries in Quantum Field Theory in d ≥ 3 have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta defects, which generalize the notion of theta-angles, and allow the construction of universal and non-universal topological symmetry defects. We complement this physical analysis by proposing a mathematical framework (based on higher-fusion categories) that converts the physical construction of non-invertible symmetries into a concrete computational scheme.

  • 37.
    Bhattacharya, Sayan
    et al.
    Univ Warwick, Dept Comp Sci, Coventry, W Midlands, England..
    Chakrabarty, Deeparnab
    Dartmouth Coll, Dept Comp Sci, Hanover, NH 03755 USA..
    Henzinger, Monika
    Univ Vienna, Fac Comp Sci, Vienna, Austria..
    Na Nongkai, Danupon
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Theoretical Computer Science, TCS.
    Dynamic Algorithms for Graph Coloring2018In: SODA'18: PROCEEDINGS OF THE TWENTY-NINTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, ASSOC COMPUTING MACHINERY , 2018, p. 1-20Conference paper (Refereed)
    Abstract [en]

    We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for ( δ + 1)vertex coloring and (2 δ 1)edge coloring in a graph with maximum degree δ. It is natural to ask if we can efficiently maintain such colorings in the dynamic setting as well. We get the following three results. (1) We present a randomized algorithm which maintains a ( δ+1)-vertex coloring with O(log δ) expected amortized update time. (2) We present a deterministic algorithm which maintains a (1 + o(1)) δ-vertex coloring with O(polylog δ) amortized update time. (3) We present a simple, deterministic algorithm which maintains a (2 δ)edge coloring with O(log δ) worst-case update time. This improves the recent O( δ)-edge coloring algorithm with Õ ( p δ) worst-case update time [4].

  • 38.
    Bjelle, Kajsa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    A Multi-Level Extension of the Hierarchical PCA Framework with Applications to Portfolio Construction with Futures Contracts2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    With an increasingly globalised market and growing asset universe, estimating the market covariance matrix becomes even more challenging. In recent years, there has been an extensive development of methods aimed at mitigating these issues. This thesis takes its starting point in the recently developed Hierarchical Principal Component Analysis, in which a priori known information is taken into account when modelling the market correlation matrix. However, while showing promising results, the current framework only allows for fairly simple hierarchies with a depth of one. In this thesis, we introduce a generalisation of the framework that allows for an arbitrary hierarchical depth. We also evaluate the method in a risk-based portfolio allocation setting with Futures contracts. 

    Furthermore, we introduce a shrinkage method called Hierarchical Shrinkage, which uses the hierarchical structure to further regularise the matrix. The proposed models are evaluated with respect to how well-conditioned they are, how well they predict eigenportfolio risk and portfolio performance when they are used to form the Minimum Variance Portfolio. We show that the proposed models result in sparse and easy-to-interpret eigenvector structures, improved risk prediction, lower condition numbers and longer holding periods while achieving Sharpe ratios that are at par with our benchmarks.

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  • 39.
    Björnfot, Agnes
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Fjelkestam, Sandra
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Predicting Short-term Absences of a Railway Crew using Historical Data2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Transportation via train is considered the most environmentally friendly way of traveling and is widely seen as the future of transportation. Canceled and delayed trains worsen customer satisfaction; thus, punctual trains are crucial for railway companies. One reason for canceled and delayed trains is the shortage of employees due to sickness or care of relatives, known as short-term absences. Therefore, it is important for railway companies to have reliable predictions of these. This thesis is in collaboration with SJ, the largest railway company in Sweden which offers trips all over Sweden and some other parts of northern Europe.

    The thesis predicts short-term absences with data provided by SJ, by using the machine learning methods random forest and extreme gradient boosting (XGBoost). The aim is to investigate if SJ can use machine learning algorithms and statistical analysis in their absence predictions and if it can yield better results than their current absence prediction methodology. Furthermore, the thesis identifies which factors are most important for the predictions. In addition to this, quantile regression is implemented for both methods since overestimating absenteeism could be better for avoiding employee shortage. 

    Two different datasets are used for two different tasks; one regression task to predict the number of absent employees on each date and one classification task to predict the probability of an absent employee on a specific duty, and then adding the probabilities to achieve the total predicted number of absent employees on each date. Both task formulations yielded good absence prediction results. XGBoost resulted overall in lower errors than random forest, meaning it was a slightly better model to implement for this task. When comparing the results, the performance for the developed models was better than the current predictions at SJ, meaning machine learning models could benefit SJ's prediction work.

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  • 40.
    Blok, Sander
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Nonlinear Parametid Model Order Reduction2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Model order reduction techniques are a powerful tool to ease the computational burden of simulating complex systems. By reducing the dimensionality of high-fidelity models, while preserving essential system dynamics, model order reduction enables faster and more efficient simulations without compromising accuracy. This reduction in computational complexity enables sensitivity analysis, optimization, and control design of complex systems making it particularly beneficial for time-critical applications that require real-time or near-real-time simulations.

    Projection-based model order reduction is a prominent rechnique in the field of model order reduction which involves constructing a reduced basis from the original system and projecting the system dynamics onto a small number of generalized states. A popular method for nonlinear systems is the Proper Orthogonal Decomposition which computes this basis based on pre-computed snapshots of the solution in an offline stage. However, unless the reduced operators can be pre-computed, the cost of projection-based model order reduction still scales with the size of the high-fidelity model and potentially fails to yield significant computational improvements. Until recently, most methods for reducing the evaluation costs of nonlinearities relied on empirical methods, like the Empirical Interpolation Method, which operate on the continuous formulation. COMSOL Multiphysics has a clear separation between the continuous formulation, with its direct access to the weak form, and the discretization, hidden in the core code. While this software enables flexible nonlinear extensions and modifications of the problem, this design makes equation-based model order reduction on the continuous level challenging.

    The objective of this thesis is to assess the feasibility of implementing state-of-the-art nonlinear model order reduction techniques within COMSOL Multiphysics. Numerical experiments are conducted to validate and evaluate the effectiveness of the proposed techniques. Furthermore, we propose in this thesis a method to stabilize general saddle point problems, which has been successfully tested on a structural mechanics problem involving a nearly incomplressible nonlinear material.

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  • 41.
    Blommegård, Oscar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The Impact of the Retrieval Text Set for Text Sentiment Classification With the Retrieval-Augmented Language Model REALM2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Large Language Models (LLMs) have demonstrated impressive results across various language technology tasks. By training on large corpora of diverse text collections from the internet, these models learn to process text effectively, allowing them to acquire comprehensive world knowledge. However, this knowledge is stored implicitly in the parameters of the model, and it is necessary to train ever-larger networks to capture more information. Retrieval-augmented language models have been proposed as a way of improving the interpretability and adaptability of normal language models by utilizing a separate retrieval text set during application time. These models have demonstrated state-of-the-art results on knowledge-intensive tasks such as question-answering and fact-checking. However, their effectiveness in text classification remains unexplored. This study investigates the impact of the retrieval text set on the performance of the retrieval-augmented language model REALM model for sentiment text classification tasks. The results indicate that the addition of retrieval text data fails to improve the prediction capabilities of REALM for sentiment text classification tasks. This outcome is mainly due to the difference in functionality of the retrieval mechanisms during pre-training and fine-tuning. During pre-training, the neural knowledge retriever focuses on retrieving factual knowledge such as dates, cities and names to enhance the prediction of the model. During fine-tuning, the retriever aims to retrieve texts that can strengthen the prediction of the text sentiment classification task. The findings suggest that retrieval models may hold limited potential to enhance performance for text sentiment classification tasks.

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  • 42.
    Book, Emil
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Gnem, Emil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ensemble Models for Trend Investing2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Portfolio strategies focusing on following the trend, so called momentum based strategies, have been popular for a long time among investors and have had many academic studies, however with varying results. This study sets out to investigate different momentum trading signals as well as combining them in ensemble models such as Random Forest and the unique Dim Switch portfolio and then compare them to set benchmarks. Only one of the benchmarks, the 100% equity portfolio, is found to have better returns than the constructed momentum based strategies, however the momentum based strategies show a lot of potential with high risk-adjusted returns and good performance with regards to Expected Shortfall, Value at Risk and Maximum Drawdown. The most common momentum trading signal, the momentum rule with 9 months lookback, was found to have the highest risk-adjusted returns compared to both the benchmarks and the ensemble models, but it was also found to have slightly heavier left tail than the ensemble models.

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  • 43.
    Borg, Magnus
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ternqvist, Lucas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Risk Management and Sustainability - A Study of Risk and Return in Portfolios With Different Levels of Sustainability2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis examines the risk profile of Electronically Traded Funds and the dependence of the ESG rating on risk. 527 ETFs with exposure globally were analyzed. Risk measures considered were Value-at-Risk and Expected Shortfall, while some other metrics of risk was used, such as the volatility, maximum drawdown, tail dependece, and copulas. Stress tests were conducted in order to test the resilience against market downturns. The ETFs were grouped by their ESG rating as well as by their carbon intensity. The results show that the lowest risk can be found for ETFs with either the lowest ESG rating or the highest. Generally, a higher ESG rating implies a lower risk, but without statistical significance in many cases. Further, ETFs with a higher ESG rating showed, on average, a lower maximum drawdown, a higher tail dependence, and more resilience in market downturns. Regarding volatility, the average was shown to be lower on average for ETFs with a higher ESG rating, but no statistical significance could be found. Interestingly, the results show that investing sustainably returns a better financial performance at a lower risk, thus going against the Capital Asset Pricing Model.

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  • 44.
    Bortolin, Gianantonio
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Gutman, Per-Olof
    A new algorithm for variable selection2006In: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, p. 1309-1314Conference paper (Refereed)
    Abstract [en]

    A new method for variable selection and estimation called Iteratively Scaled Ridge Regression, ISRR, is proposed. The method is an iterative algorithm based on ridge regression. Simulation studies show that ISRR shares the properties of both subset selection and ridge regression. It selects an optimal subset of the regressor variables and is robust to small changes in the data set. The ISRR algorithm was primarily developed for linear models, but is quite simple and general and can easily be extended to more general linear and nonlinear models.

  • 45.
    Bradinoff, Nedialko Stoyanov
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Benfords law and the characteristic Polynomial of a CUE Matrix2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Benford’s Law describes a profound behavior that the leading digits of many quantities arising from mathematics, physics, finance, and engineering exhibit. In this text we prove Benford’s Law for the absolute value of the characteristic polynomial det (U-λI) of the CUE(N) as N →∞.  Our analysis produces an integrable bound for the characteristic function of log | det (U - λI|.

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  • 46.
    Breiten, Tobias
    et al.
    Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität, Graz, 8010, Austria.
    Ringh, Emil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Residual-based iterations for the generalized Lyapunov equation2019In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 59, no 4, p. 823-852Article in journal (Refereed)
    Abstract [en]

    This paper treats iterative solution methods for the generalized Lyapunov equation. Specifically, a residual-based generalized rational-Krylov-type subspace is proposed. Furthermore, the existing theoretical justification for the alternating linear scheme (ALS) is extended from the stable Lyapunov equation to the stable generalized Lyapunov equation. Further insights are gained by connecting the energy-norm minimization in ALS to the theory of H2-optimality of an associated bilinear control system. Moreover it is shown that the ALS-based iteration can be understood as iteratively constructing rank-1 model reduction subspaces for bilinear control systems associated with the residual. Similar to the ALS-based iteration, the fixed-point iteration can also be seen as a residual-based method minimizing an upper bound of the associated energy norm.

  • 47.
    Brolin, Alice
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Möbius and Loewner energy on curves with corners2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The Möbius energy and the Loewner energy are two Möbius invariant quantaties defined for Jordan curves. We start by introducing some of the basic properties of these two energies. Both are finite if and only if the curves belong to a class called Weil-Petersson. The Weil-Petersson class does not contain curves with corners. In part motivated by recent work of Johansson and Viklund we introduce regularized versions of both the Mövius and Loewner energy which allow for certain curves with isolated corners. We also look at the derivative of the Loewner energy.

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  • 48.
    Brunnberg, Aston
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Holte, Gustaf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Survival Comparison of Open and Endovascular Repair Using Machine Learning2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Today there exists two types of preventive surgical treatment procedures for Abdominal Aortic Aneurysm. In order to make an informed choice of treatment, the clinician needs to have a clear picture of how the choice will affect the patients chances of survival. In this master thesis, machine learning techniques are used to predict survival probabilities after respective treatment procedure and the performance is compared to the more conventional Kaplan-Meier estimator. 

    Using Danish patient data, different machine learning models for survival predictions were trained and evaluated by their performance. Administrative Brier Score was used as performance metric as the data was administratively censored. An Ensemble model consisting of one Random Survival Forest and one Neural Multi Task Logistic Regression model was shown to achieve the best performance and significantly outperformed the conventional Kaplan-Meier model.

    Furthermore, an approach to investigate the predicted effects of choice of treatment was introduced. It showed that on average the Ensemble model predicted the choice of treatment to have less effect on the long term survival than what the corresponding prediction using the Kaplan-Meier estimator suggested. This applies to the full patient group as well as for patients of age between 70 and 79 years. In the latter case this prediction was also shown to be more accurate.

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  • 49.
    Cao, Buqing
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Dynamic Portfolio Management by Market Cycle Identification and Inter-Market Analysis2020Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In recent decades, the 2000 dot-com bubble burst, 2008 financial crisis, and 2020 COVID-19 pandemic selloff have been the three primary financial crises in the financial markets. Ray Dalio, a US hedge fund manager, suggested building an All-Weather Portfolio with mixed asset classes. So it can generate a stable return through different market conditions. However, his portfolio also failed in the recent pandemic selloff. The thesis aims to construct a portfolio that can outperform the benchmark and identify the recent market crisis. By understanding the financial market deeply and studying the monetary policy changes, the dynamic portfolio has been created and simulated step by step. As a result, the dynamic portfolio can time the financial market in the current market condition and generate an extra return to outperform the benchmark. The dynamic portfolio does not necessarily work in the future. The current monetary system needs to remain stable. So the future monetary policies will be useful, facing market uncertainties and the coming end of the long-term debt cycle.

  • 50.
    Carlsson, Simon
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Regnell, August
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Reinforcement Learning for Market Making2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Market making – the process of simultaneously and continuously providing buy and sell prices in a financial asset – is rather complicated to optimize. Applying reinforcement learning (RL) to infer optimal market making strategies is a relatively uncharted and novel research area. Most published articles in the field are notably opaque concerning most aspects, including precise methods, parameters, and results. This thesis attempts to explore and shed some light on the techniques, problem formulations, algorithms, and hyperparameters used to construct RL-derived strategies for market making. First, a simple probabilistic model of a limit order book is used to compare analytical and RL-derived strategies. Second, a market making agent is trained on a more complex Markov chain model of a limit order book using tabular Q-learning and deep reinforcement learning with double deep Q-learning. Results and strategies are analyzed, compared, and discussed. Finally, we propose some exciting extensions and directions for future work in this research field.

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