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  • 201.
    Larson, Ellis
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Volatility Forecasting using GARCH Processes with Exogenous Variables2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Volatility is a measure of the risk of an investment and plays an essential role in several areas of finance, including portfolio management and pricing of options. In this thesis, we have implemented and evaluated several so-called GARCH models for volatility prediction based on historical price series. The evaluation builds on different metrics and uses a comprehensive data set consisting of many assets of various types. We found that more advanced models do not, on average, outperform simpler ones. We also found that the length of the historical training data was critical for GARCH models to perform well and that the length was asset-dependent. Further, we developed and tested a method for taking exogenous variables into account in the model to improve the predictive performance of the model. This approach was successful for some of the large US/European indices such as Russell 2000 and S&P 500.

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  • 202.
    Larsson, Malkolm
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lövgren, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Viability Evaluation of the Turtle Trading Rules on Major Market Indexes2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The Turtle Trading Rules was a successful trend-following trading strategy for commodities in the 1980s but has lost recognition in recent days. The strategy revolved around rules for entering and exiting trades as well as position sizing for each trade. The rules was based on the fundamental aim to capture market trends while at the same time maintaining a controlled risk exposure. This thesis aims to revise the Turtle Trading Rules, here applied on major market indexes, and to examine its viability through different financial metrics. This is done by first implementing the aforementioned trading strategy to the indexes, and later by synthesizing market data through Geometric Brownian Motions. The latter primarily to examine how the strategy perform in different financial environments, what market traits favor the strategy, and to complement the previous examination without altering the core principles of the Turtle Trading Rules. The results suggest that the revised rules for major market indexes is not viable. This because of the poor return, the highest achieved 20-year return and average annual return was 25.1 % and 1.4% respectively (without taking trading fees into account). Furthermore, the strategy applied on synthetic data suggests that favorable traits are highly cyclical data with low volatility, which seldom is the case for real financial time series. The results further indicate that the main issue lies in the rules not being able to distinguish noise from actual entry and exit triggers. Moreover, the drawdown further suggest that it is the exit rather than the entry rules that are to blame for the poor performance during the cycle of a trade.

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  • 203.
    Lavatt, Rafael
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A Neural Network Approach for Generating Investors’ Views in the Black-Litterman Model2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis investigates how neural networks can be used to produce investors' views for the Black-Litterman market model. The study uses two data sets, one with global stock market indexes and one with stock market data from the S&P 500. The task of the neural networks is to produce forecasts for the returns for the next quarter and the following year. The neural network will have to predict whether the market will move up or down and determine if the market movement is less than or equal to one standard deviation, creating four different scenarios. The forecasts are used as input to the Black-Litterman model to generate new portfolios, which are backtested from 2017 until 2022. The index data set was compared to a benchmark portfolio and a portfolio with naive risk diversification, while the S&P 500 data set was compared to market capitalization-weighted and naive portfolios. This resulted in eight different backtests where the neural networks obtained AUC values in the range of 0.56-0.73 and prediction accuracies in the range of 20.9% - 42.1%. The network used for yearly predictions on the index data set was the only network to outperform the benchmark portfolio. It obtained a Sharpe ratio of 1.782, a Sortino ratio of 2.165, and a maximum drawdown of -30.9% compared to the benchmark portfolio, where the corresponding metrics were 1.544, 1.879, and -32.8%.

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  • 204.
    Leatherman, Tori
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Link Prediction Using Learnable Topology Augmentation2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Link prediction is a crucial task in many downstream applications of graph machine learning. Graph Neural Networks (GNNs) are a prominent approach for transductive link prediction, where the aim is to predict missing links or connections only within the existing nodes of a given graph. However, many real-life applications require inductive link prediction for the newly-coming nodes with no connections to the original graph. Thus, recent approaches have adopted a Multilayer Perceptron (MLP) for inductive link prediction based solely on node features. In this work, we show that incorporating both connectivity structure and features for the new nodes provides better model expressiveness. To bring such expressiveness to inductive link prediction, we propose LEAP, an encoder that features LEArnable toPology augmentation of the original graph and enables message passing with the newly-coming nodes. To the best of our knowledge, this is the first attempt to provide structural contexts for the newly-coming nodes via learnable augmentation under inductive settings. Conducting extensive experiments on four real- world homogeneous graphs demonstrates that LEAP significantly surpasses the state-of-the-art methods in terms of AUC and average precision. The improvements over homogeneous graphs are up to 22% and 17%, respectively. The code and datasets are available on GitHub*.

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  • 205.
    Lechner, Vincent
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Image-based Mapping of Regional Relative Pressures Using the Pressure Poisson Equation - Evaluations on Dynamically Varying Domains in a Cardiovascular Setting2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this project, the inverse problem of determining regional pressure variations from measured blood velocity data in the contect of a cardiovascular setting has been approached. A common esimator, the pressure poisson estimator (PPE) has been implemented in a non-variational setting and evaluated for clinically relevant synthetic flow cases, over dynamically varying domains, mimicking or directly representing the intra-cardiac space: A synthetic dynamic domain benchmark problem and a patient specific model of the left ventricle. The results obtained show under ideal condition the capability of the approach to tackle complex domains successfully and to obtain regional pressure fields to a high degree of accuracy when compared to a locally provided state of the art estimator, the stokes estimator (STE). Under noise, results obtained suggest that divergence may occur with finer temporal resolution. Spatially convergence in a setting mimicking an image scenario is observed with minor exceptions though to stem from the specific composition of the flow field between discretizations. The implementation at hand avoids common problems in the non-variational approaches of this estimator stemming from domain complexity and leads to a simple application of the pure neumann boundary conditions required to compute the relative pressure field while avoiding the need to estimate boundary normals or use an embedded approach. The resulting linear system has desirable properties such as symmetry and compliance with the discrete compatibility condition by construction.

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  • 206.
    Lenells, Jonatan
    Lund University, Sweden .
    Classification of all travelling-wave solutions for some nonlinear dispersive equations2007In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 365, no 1858, p. 2291-2298Article in journal (Refereed)
    Abstract [en]

    We present a method for the classification of all weak travelling-wave solutions for some dispersive nonlinear wave equations. When applied to the Camassa-Holm or the Degasperis-Procesi equation, the approach shows the existence of not only smooth, peaked and cusped travelling-wave solutions, but also more exotic solutions with fractallike wave profiles.

  • 207.
    Lenells, Jonatan
    Baylor University, United States .
    Spheres, Kähler geometry and the Hunter-Saxton system2013In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 469, no 2154, article id 20120726Article in journal (Refereed)
    Abstract [en]

    Many important equations of mathematical physics arise geometrically as geodesic equations on Lie groups. In this paper, we study an example of a geodesic equation, the two-component Hunter- Saxton (2HS) system, which displays a number of unique geometric features. We show that 2HS describes the geodesic flow on a manifold, which is isometric to a subset of a sphere. Since the geodesics on a sphere are simply the great circles, this immediately yields explicit formulae for the solutions of 2HS.We also show thatwhen restricted to functions of zero mean, 2HS reduces to the geodesic equation on an infinite-dimensional manifold, which admits a Kähler structure. We demonstrate that this manifold is in fact isometric to a subset of complex projective space, and that the above constructions provide an example of an infinite-dimensional Hopf fibration.

  • 208.
    Lenells, Jonatan
    Baylor University, United States .
    The Degasperis-Procesi equation on the half-line2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 76, no 1, p. 122-139Article in journal (Refereed)
    Abstract [en]

    We analyze a class of initial-boundary value problems for the Degasperis-Procesi equation on the half-line. Assuming that the solution u(x,t) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann-Hilbert problem formulated in the plane of the complex spectral parameter k.

  • 209.
    Lenells, Jonatan
    et al.
    Baylor University, United States .
    Wunsch, M.
    The Hunter-Saxton System and the Geodesics on a Pseudosphere2013In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 38, no 5, p. 860-881Article in journal (Refereed)
    Abstract [en]

    We show that the two-component Hunter-Saxton system with negative coupling constant describes the geodesic flow on an infinite-dimensional pseudosphere. This approach yields explicit solution formulae for the Hunter-Saxton system. Using this geometric intuition, we conclude by constructing global weak solutions. The main novelty compared with similar previous studies is that the metric is indefinite.

  • 210.
    Leopold, Lina
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Random matrix theory in machine learning2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis, we review some applications of random matrix theory in machine learning and theoretical deep learning. More specifically, we review data modelling in the regime of numerous and large dimensional data, a method for estimating covariance matrix distances in the aforementioned regime, as well as an asymptotic analysis of a simple neural network model in the limit where the number of neurons is large and the data is both numerous and large dimensional. We also review some recent research where random matrix models and methods have been applied to Hessian matrices of neural networks with interesting results. As becomes apparent, random matrix theory is a useful tool for various machine learning applications and it is a fruitful field of mathematics toexplore, in particular, in the context of theoretical deep learning.

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  • 211.
    Li, Julia
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Individual Claims Modelling with Recurrent Neural Networks in Insurance Loss Reserving2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Loss reserving in P&C insurance, is the common practice of

    estimating the insurer’s liability from future claims it will have to

    pay out on. In the recent years, it has been popular to explore the

    options of forecasting this loss with the help of machine learning

    methods. This is mainly attributed to the increase in computational

    power, opening up opportunities for handling more complex computations

    with large datasets. The main focus of this paper is to implement and

    evaluate a recurrent neural network called the deeptriangle by Kuo for

    modelling payments of individual reported but not settled claims. The

    results are compared with the traditional Chain Ladder method and a

    baseline model on a simulated dataset provided by Wüthrich’s simulation

    machine.  The models were implemented in Python using Tensorflow’s

    functional API. The results show that the recurrent neural network does

    not outperform the Chain Ladder method on the given data. The recurrent

    neural network is weak towards the sparse and chaotic nature of

    individual claim payments and is unable to detect a stable sequential

    pattern. Results also show that the neural network is prone to

    overfitting, which can theoretically be compensated with larger dataset

    but comes at a cost in terms of feasibility.

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  • 212.
    Liljemalm, Rickard
    KTH, School of Technology and Health (STH), Medical Engineering, Neuronic Engineering.
    Infrared Laser Stimulation of Cerebral Cortex Cells - Aspects of Heating and Cellular Responses2013Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The research of functional stimulation of neural tissue is of great interest within the field of clinical neuroscience to further develop new neural prosthetics. A technique which has gained increased interest during the last couple of years is the stimulation of nervous tissue using infrared laser light. Successful results have been reported, such as stimulation of cells in both the central nervous system, and in the peripheral nervous system, and even cardiomyocytes. So far, the details about the stimulation mechanism have been a question of debate as the mechanism is somewhat hard to explain. The mechanism is believed to have a photo-thermal origin, where the light from the laser is absorbed by water, thus increasing the temperature inside and around the target cell. Despite the mechanism questions, the technique holds several promising features compared to traditional electrical stimulation. Examples of advantages are that it is contact free, no penetration is needed, it has high spatial resolution and no toxic electrochemical byproducts are produced during stimulation. However, since the laser pulses locally increase the temperature of the tissue, there is a risk of heat induced damage. Therefore, the effect of increased temperatures must be investigated thoroughly. One method of examining the changes in temperature during stimulation is to model the heating.

    This thesis is based on the work from four papers with the main aim to investigate and describe the response of heating, caused by laser pulses, on central nervous system cells. In paper one, a model of the heating during pulsed laser stimulation is established and used to describe the dynamic temperature changes occurring during functional stimulation of cerebral cortex cells. The model was used in all four papers. Furthermore, single cell responses, as action potentials, as well as network responses, as activity inhibition, were observed. In paper two, the response of rat astrocytes exposed to laser induced hyperthermia was investigated. Cellular migration was observed and the migration limit was used to calculate the kinetic parameters for the cells, i.e., the reaction activation energy, Ea (321.4 kJmol-1), and the frequency factor, Ac (9.47 x 1048 s-1). Furthermore, a damage signal ratio (DSR) for calculating a threshold for cellular damage was defined, and calculated to six percent. In paper three, the response of hyperthermia to cerebral cortex cells was investigated, in the same way as in the second paper. Fluorescence staining of the metabolic activity was used to reveal the heat response, and by using the limit of the observed increased fluorescence the kinetic parameters, Ea (333.6 kJmol-1), and Ac (9.76 x 1050 s-1), were calculated. The DSR for the cells was calculated to five percent. In paper four, the behavior of action potentials triggered by laser stimulation was investigated. More specifically, the time delay from the start of a laser pulse to the detection of an action potential, delta-t, were investigated. Two different behaviors for the initial action potentials were observed: fast decreasing delta-t and slow decreasing delta-t. The results show the dynamic behavior of action potential responses to infrared light.

    The work of this thesis show the dynamic changes of the temperature during optical stimulation, using an infrared laser working at 1,550 nanometers. It also shows how the changes cause astrocytes to migrate for pulses several seconds long, and neurons to fire action potentials for pulses in the millisecond range. Furthermore, a damage signal ratio was defined and calculated for the cell systems.

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  • 213.
    Liljemalm, Rickard
    et al.
    KTH, School of Technology and Health (STH), Medical Engineering, Neuronic Engineering.
    Nyberg, Tobias
    KTH, School of Technology and Health (STH), Medical Engineering, Neuronic Engineering.
    Quantification of a Thermal Damage Threshold for Astrocytes Using Infrared Laser Generated Heat Gradients2014In: Annals of Biomedical Engineering, ISSN 0090-6964, E-ISSN 1573-9686, Vol. 42, no 4, p. 822-832Article in journal (Refereed)
    Abstract [en]

    The response of cells and tissues to elevated temperatures is highly important in several research areas, especially in the area of infrared neural stimulation. So far, only the heat response of neurons has been considered. In this study, primary rat astrocytes were exposed to infrared laser pulses of various pulse lengths and the resulting cell morphology changes and cell migration was studied using light microscopy. By using a finite element model of the experimental setup the temperature distribution was simulated and the temperatures and times to induce morphological changes and migration were extracted. These threshold temperatures were used in the commonly used first-order reaction model according to Arrhenius to extract the kinetic parameters, i.e., the activation energy, E (a), and the frequency factor, A (c), for the system. A damage signal ratio threshold was defined and calculated to be 6% for the astrocytes to change morphology and start migrating.

  • 214.
    Linusson, Svante
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Potka, Samu
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Properties of the edelman-greene bijection (extended abstract)2018In: FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics , 2018, article id 79Conference paper (Refereed)
    Abstract [en]

    Edelman and Greene constructed a bijective correspondence between the reduced words of the reverse permutation in the symmetric group Sn and standard Young tableaux of the staircase shape (n - 1, n - 2,..., 1). Our motivation originates from random sorting networks, a line of research initiated by Angel, Holroyd, Romik and Virág. We reformulate one of their conjectures on the shapes of intermediate configurations coming from random sorting networks. Properties of the Edelman-Greene bijection restricted to 132-avoiding and 2143-avoiding permutations are presented. We also consider the Edelman-Greene bijection applied to non-reduced words.

  • 215.
    Liu, Bing
    et al.
    School of Transportation Science and Engineering, Beihang University, Beijing 100191, People's Republic of China.
    Ma, Xiaolei
    School of Transportation Science and Engineering, Beihang University, Beijing 100191, People's Republic of China; Key Laboratory of Intelligent Transportation Technology and System, Ministry of Education, Beijing 100191, People's Republic of China.
    Tan, Erlong
    School of Transportation Science and Engineering, Beihang University, Beijing 100191, People's Republic of China.
    Ma, Zhenliang
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Transport planning.
    Passenger flow anomaly detection in urban rail transit networks with graph convolution network-informer and Gaussian Bayes models2023In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 381, no 2254, article id 20220253Article in journal (Refereed)
    Abstract [en]

    Passenger flow anomaly detection in urban rail transit networks (URTNs) is critical in managing surging demand and informing effective operations planning and controls in the network. Existing studies have primarily focused on identifying the source of anomalies at a single station by analysing the time-series characteristics of passenger flow. However, they ignored the high-dimensional and complex spatial features of passenger flow and the dynamic behaviours of passengers in URTNs during anomaly detection. This article proposes a novel anomaly detection methodology based on a deep learning framework consisting of a graph convolution network (GCN)-informer model and a Gaussian naive Bayes model. The GCN-informer model is used to capture the spatial and temporal features of inbound and outbound passenger flows, and it is trained on normal datasets. The Gaussian naive Bayes model is used to construct a binary classifier for anomaly detection, and its parameters are estimated by feeding the normal and abnormal test data into the trained GCN-informer model. Experiments are conducted on a real-world URTN passenger flow dataset from Beijing. The results show that the proposed framework has superior performance compared to existing anomaly detection algorithms in detecting network-level passenger flow anomalies. This article is part of the theme issue 'Artificial intelligence in failure analysis of transportation infrastructure and materials'.

  • 216.
    Ljungström, Zacharias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Assessing the Impact of Tracking Data on Passing Metrics in Football2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In recent years, data analysis in football has become an essential tool for evaluating the performance of teams and players. A variety of metrics, detecting different properties, are being used to gain the optimal advantage. These metrics have mostly been based on event data, but tracking data is becoming more available, providing a new level of context when incorporated into the models. In this thesis, this effect on passes, the most frequent action in football, have been investigated. This has been done by creating expected threat models, using logistic regression and neural networks, and comparing their performances, with and without tracking data.

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  • 217.
    Lord, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    From Relations to Simplicial Complexes: A Toolkit for the Topological Analysis of Networks2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. Correspondences between relations and graphs are given and a brief introduction to graph theory is followed by a more detailed study of cohesiveness and centrality. We show how graph degeneracy is equivalent to the concept of k-cores, which give a measure of the cohesiveness or interconnectedness of a subgraph. We then further extend this to d-cores of directed graphs. After a brief introduction to topology, focusing on topological spaces from distances, we present a historical discussion on the early developments of algebraic topology. This is followed by a more formal introduction to simplicial homology where we define the homology groups. In the context of algebraic topology, the d-cores of a digraph give rise to a partially ordered set of subgraphs, leading to a set of filtrations that is two-dimensional in nature. Directed clique complexes of digraphs are defined in order to encode the directionality of complete subdigraphs. Finally, we apply these methods to the neuronal network of C.elegans. Persistent homology with respect to directed core filtrations as well as robustness of homology to targeted edge percolations in different directed cores is analyzed. Much importance is placed on intuition and on unifying methods of such dispersed disciplines as sociology and network neuroscience, by rooting them in pure mathematics.

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  • 218.
    Lorenzo Varela, Juan Manuel
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, System Analysis and Economics.
    Parameter bias in misspecified HCM: An empirical study.2018Conference paper (Refereed)
    Abstract [en]

    Model misspecification is likely to occur when working with real datasets. However, previous studies showing the advantages of the hybrid choice models have mostly used models where structural and measurement equations match the functions employed in the data generating process, especially when parameter biases were discussed.

     

    The aim of this paper is to investigate the extent of parameter bias in misspecified hybrid choice models. For this task, a mode choice model is estimated on synthetic data with efforts focus on mimicking the conditions present in real datasets, where the postulated structural and measurement equations are less flexible than the functions used for the data generating process.

     

    Results show that hybrid choice models, even if misspecified, manage to recover better parameter estimates than a multinomial logit. However, hybrid choice models are not unbeatable, as results indicate that misspecified hybrid choice models might still yield biased parameter estimates. Moreover, results suggest that hybrid choice models successfully isolate the source of model bias, preventing its propagation to other parameter estimates. Results also show that parameter estimates from hybrid choice models are sensible to modelling assumptions, and that parameter estimates of the utility function are robust, given that errors are modelled.

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  • 219.
    Lorenzo Varela, Juan Manuel
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, System Analysis and Economics. Grupo de Ferrocarriles y Transportes , Universidad de A Coruña, España.
    Orro Arcay, Alfonso
    Grupo de Ferrocarriles y Transportes , Universidad de A Coruña, España.
    Coeficientes aleatorios con distribución triangular asimétrica en modelos logit mixto.2014Conference paper (Refereed)
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  • 220.
    Lu, Billy
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Prediction of Short-term Default Probability of Credit Card Invoices Using Behavioural Data2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Probability of Default (PD) is a standard metric to model and monitor credit risk, a major risk facing financial institutions. Traditional PD models are used to forecast risk levels in the long-term, while short-term PD predictions are rarer, but they can support management decisions on an operational level. This thesis investigates the potential usage of short-term PD for credit card invoices within the invoice-to-cash process involving cash-collection activities, such as reminders and calls to customers. A model of this sort enables customized cash-collection efforts that are adapted to different credit card holders. Specifically, the main objectives of this thesis are to examine the usability of machine learning techniques in predicting the short-term default probability of credit card invoices and to investigate what features of credit card holders are important for default prediction.

    The data set was collected from SEB Kort Bank AB, a payment card company operating in the Nordics, and it consists of overdue credit card invoices with belonging customer behavioural data. Customer behavioural data includes historical purchase patterns, customer information and event variables etc. The data is severely imbalanced with much fewer default invoices than non-default invoices. The features were selected using filter methods and correlation analysis. Several machine learning algorithms, including logistic regression, decision trees, random forest, CatBoost and XGBoost, were tested along with various resampling techniques, such as undersampling and SMOTE to treat class imbalances. 

    The results were primarily evaluated using Precision-Recall AUC and F-score. The two best-performing models had a Precision-Recall AUC and an F-score of 0.304 and 0.332, respectively. The ROC-AUC was roughly 0.89 for both models. Both models were trained using CatBoost. The results obtained suggest a fair performance for the default class (but superior to a baseline model) and a high performance for the non-default class. Moreover, it was shown that the cut-off probability threshold is a key aspect of classifying an invoice as default or non-default and should be adjusted after preference based on a precision-recall trade-off. Furthermore, feature importance was evaluated using two metrics, i.e, how much on average a prediction changes when the feature changes, and how much the loss value changes when the feature is included or excluded. The main finding in terms of feature importance is that event variables are not critical. The observed important predictive features include credit card balances, card activities, credit utilization and the number of historical invoice payments. Further research is recommended to draw definite conclusions in this regard.

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  • 221.
    Lundin, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Metrics for Multidimensional Persistence2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    A fundamental mathematical object in topological data analysis today is the persistence module. This thesis explores different metrics on multidimensional persistence modules, where spaces are parametrized along multiple dimensions. The focus is especially on metrics constructed by the use of so called noise systems, introduced by Scolamiero et al. in 2015. Furthermore, suggestions for new noise systems are given and bounds for their metrics are presented. An exact computation for the metric induced by the volume noise system is also shown for pairs of modules satisfying certain conditions.

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  • 222.
    Maksymchuk Netterström, Nazar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Unauthorised Session Detection with RNN-LSTM Models and Topological Data Analysis2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis explores the possibility of using session-based customers data from Svenska Handelsbanken AB to detect fraudulent sessions. Tools within Topological Data Analysis are employed to analyse customers behavior and examine topological properties such as homology and stable rank at the individual level. Furthermore, a RNN-LSTM model is, on a general behaviour level, trained to predict the customers next event and investigate its potential to detect anomalous behavior. The results indicate that simplicial complexes and their corresponding stable rank can be utilized to describe differences between genuine and fraudulent sessions on individual level. The use of a neural network suggests that there are deviant behaviors on general level concerning the difference between fraudulent and genuine sessions. The fact that this project was done without internal bank knowledge of fraudulent behaviour or historical knowledge of general suspicious activity and solely by data handling and anomaly detection shows great potential in session-based detection. Thus, this study concludes that the use of Topological Data Analysis and Neural Networks for detecting fraud and anomalous events provide valuable insight and opens the door for future research in the field. Further analysis must be done to see how effectively one could detect fraud mid-session.

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  • 223.
    Mannberg, Noah
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hierarchical Control of Simulated Aircraft2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis investigates the effectiveness of employing pretraining and a discrete "control signal" bottleneck layer in a neural network trained in aircraft navigation through deep reinforcement learning. The study defines two distinct tasks to assess the efficacy of this approach. The first task is utilized for pretraining specific parts of the network, while the second task evaluates the potential benefits of this technique. The experimental findings indicate that the network successfully learned three main macro actions during pretraining. flying straight ahead, turning left, and turning right, and achieved high rewards on the task. However, utilizing the pretrained network on the transfer task yielded poor performance, possibly due to the limited effective action space or deficiencies in the training process. The study discusses several potential solutions, such as incorporating multiple pretraining tasks and alterations of the training process as avenues for future research. Overall, this study highlights the challanges and opportunities associated with combining pretraining with a discrete bottleneck layer in the context of simulated aircraft navigation using reinforcement learning.

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  • 224.
    Mannerskog, Niklas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Forecasting Price Direction Using Different Sampling Methods2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    To extract usable information from financial data the prices of financial instruments must be summarized in an efficient manner. Typically price quotes are sampled at discrete and equidistant points in time to create a time series of prices at fixed times. However, alternative methods that instead utilize certain changes in the price data, such as price changes or drawdowns, could potentially create time series with more relevant information. This thesis builds upon previous research on so called ”directional changes” to establish scaling laws using such alternative sampling methods. This has been studied extensively for foreign exchange rates, and some of those results are replicated in this thesis. But here we also extend the results to a new domain of instruments, namely futures. In addition, data sampled with different methods is investigated for predictability using a simple classifier for forecasting trend direction. The main findings are that the aforementioned scaling laws hold for the time period investigated (2016-2020), and that using other methods than the typical discrete time method yields a more predictable time series when it comes to price trend.

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  • 225.
    Maråk, Rasmus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Trajectory Optimisation of a Spacecraft Swarm Maximising Gravitational Signal2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Proper modelling of the gravitational fields of irregularly shaped asteroids and comets is an essential yet challenging part of any spacecraft visit and flyby to these bodies. Accurate density representations provide crucial information for proximity missions, which rely heavily on it to design safe and efficient trajectories. This work explores using a spacecraft swarm to maximise the measured gravitational signal in a hypothetical mission around the comet 67P/Churyumov-Gerasimenko. Spacecraft trajectories are simultaneously computed and evaluated using a high-order numerical integrator and an evolutionary optimisation method to maximise overall signal return. The propagation is based on an open-source polyhedral gravity model using a detailed mesh of 67P/C-G and considers the comet’s sidereal rotation. We compare performance on various mission scenarios using one and four spacecraft. The results show that the swarm achieved an expected increase in coverage over a single spacecraft when considering a fixed mission duration. However, optimising for a single spacecraft results in a more effective trajectory. The impact of dimensionality is further studied by introducing an iterative local search strategy, resulting in a generally improved robustness for finding efficient solutions. Overall, this work serves as a testbed for designing a set of trajectories in particularly complex gravitational environments, balancing measured signals and risks in a swarm scenario.

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  • 226. Matoušek, J.
    et al.
    Sedgwick, E.
    Tancer, Martin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Wagner, U.
    Untangling two systems of noncrossing curves2013In: Graph Drawing: 21st International Symposium, GD 2013, Bordeaux, France, September 23-25, 2013, Revised Selected Papers, Springer, 2013, p. 472-483Conference paper (Refereed)
    Abstract [en]

    We consider two systems (α1,...,αm) and (β1,...,βn) of curves drawn on a compact two-dimensional surface ℳ with boundary. Each αi and each βj is either an arc meeting the boundary of ℳ at its two endpoints, or a closed curve. The αi are pairwise disjoint except for possibly sharing endpoints, and similarly for the βj. We want to "untangle" the βj from the αi by a self-homeomorphism of ℳ; more precisely, we seek an homeomorphism φ: ℳ → ℳ fixing the boundary of ℳ pointwise such that the total number of crossings of the αi with the φ(βj) is as small as possible. This problem is motivated by an application in the algorithmic theory of embeddings and 3-manifolds. We prove that if ℳ is planar, i.e., a sphere with h ≥ 0 boundary components ("holes"), then O(mn) crossings can be achieved (independently of h), which is asymptotically tight, as an easy lower bound shows. In general, for an arbitrary (orientable or nonorientable) surface ℳ with h holes and of (orientable or nonorientable) genus g ≥ 0, we obtain an O((m + n)4) upper bound, again independent of h and g.

  • 227.
    Maxstad, Isak
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Tactical control of unmanned aerial vehicle swarms for military reconnaissance2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The use of unmanned aerial vehicles (UAVs) is well established in the military sector with great advantages in modern warfare. The concept of using UAV swarms has been discussed over two decades, but is now seeing its first real system used by the Israel defence forces. There is no exact definition what a swarm is, but it is proposed that it should satisfy the following three requirements. A swarm should have limited human control, the number of agents in a swarm should be at least three and the agents in the swarm should cooperate to perform common tasks. The complexity of controlling multiple autonomous UAVs gives way to the problem of how to take advantage of the operators cognitive and tactical abilities to control a swarm to effectively conduct military reconnaissance missions. The method of using behaviour trees as a control structure was derived from previous work in swarm systems. A behaviour tree is a structured way of organising and prioritising actions of autonomous systems. Behaviour trees are similar to finite state machines (FSMs) with the advantages of being modular, reactive, and with better readability. Three different behaviour trees with increasing complexity was created and simulated in the game engine Unity. A fourth more real life behaviour tree was created and used as a basis for discussing the strength and weaknesses of using behaviour trees against previous work. Using behaviour tree as a unifying structure for creating a swarm that integrates the tactical abilities of an operator with the strength of an autonomous swarm seems promising. The proposed method of using behaviour trees i suggested to be used as a platform for discussing the swarm desired functions and to create a common vision for both operators and engineers how a swarm should function.

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  • 228. Mehmood, Abu Bakr
    et al.
    Shah, Umer
    KTH, School of Electrical Engineering (EES), Micro and Nanosystems.
    Shabbir, Ghulam
    A generalized approach for computing the trajectories associated with the Newtonian N body problem2006Manuscript (preprint) (Other academic)
    Abstract [en]

    The Classical Newtonian problem of describing the free motions of N gravitating bodieswhich form an isolated system in free space has been considered. It is well known from thePoincare’s Dictum that the problem is not exactly solvable. Sets of N body systems composed ofmasses having spherical symmetry, appropriate angular velocities (< 1 rad/s) and boundedposition vectors are examined. A procedure has been developed which yields expressionsapproximately defining the trajectories executed by the masses.

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  • 229. Mehmood, Abu Bakr
    et al.
    Shah, Umer
    KTH, School of Electrical Engineering (EES), Micro and Nanosystems.
    Shabbir, Ghulam
    Closed Form Approximation Solutions for the Restricted Circular Three Body Problem.2005In: Applied Sciences: APPS, E-ISSN 1454-5101, Vol. 7, no 1, p. 112-126Article in journal (Refereed)
    Abstract [en]

    An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much smaller mass than the other two. These masses perform free motion under each others’ gravitational influence. The set of solutions is found using the Lambert’s wave function.

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  • 230.
    Meisner, Patrick
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Södergren, A.
    Low-lying zeros in families of elliptic curve L-functions over function fields2022In: Finite Fields and Their Applications, ISSN 1071-5797, E-ISSN 1090-2465, Vol. 84, article id 102096Article in journal (Refereed)
    Abstract [en]

    We investigate the low-lying zeros in families of L-functions attached to quadratic and cubic twists of elliptic curves defined over Fq(T). In particular, we present precise expressions for the expected values of traces of high powers of the Frobenius class in these families with a focus on the lower order behavior. As an application we obtain results on one-level densities and we verify that these elliptic curve families have orthogonal symmetry type. In the quadratic twist families our results refine previous work of Comeau-Lapointe. Moreover, in this case we find a lower order term in the one-level density reminiscent of the deviation term found by Rudnick in the hyperelliptic ensemble. On the other hand, our investigation is the first to treat these questions in families of cubic twists of elliptic curves and in this case it turns out to be more complicated to isolate lower order terms due to a larger degree of cancellation among lower order contributions.

  • 231.
    Mickelsson, Jouko
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    FAMILIES OF DIRAC OPERATORS AND QUANTUM AFFINE GROUPS2011In: Journal of the Australian Mathematical Society, ISSN 1446-7887, E-ISSN 1446-8107, Vol. 90, no 2, p. 213-220Article in journal (Refereed)
    Abstract [en]

    Twisted K-theory classes over compact Lie groups can be realized as families of Fredholm operators using the representation theory of loop groups. In this paper we show how to deform the Fredholm family in the sense of quantum groups. The family of Dirac-type operators is parametrized by vectors in the adjoint module for a quantum affine algebra and transforms covariantly under a central extension of the algebra.

  • 232.
    Mickelsson, Jouko
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    From gauge anomalies to gerbes and gerbal actions2010In: Motives, quantum field theory, and pseudodifferential operators, Boston: Clay mathematical institute , 2010, p. 211-220Conference paper (Refereed)
  • 233.
    Mickelsson, Jouko
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    From Gauge Anomalies to Gerbes and Gerbal Representations: Group Cocycles in Quantum Theory2010In: Acta Polytechnica: Journal of Advanced Engineering, ISSN 1210-2709, Vol. 50, no 3, p. 42-47Article in journal (Refereed)
    Abstract [en]

    In this paper I shall discuss the role of group cohomology in quantum mechanics and quantum field theory. First, I recall how cocycles of degree 1 and 2 appear naturally in the context of gauge anomalies. Then we investigate how group cohomology of degree 3 comes from a prolongation problem for group extensions and we discuss its role in quantum field theory. Finally, we discuss a generalization to representation theory where a representation is replaced by a 1-cocycle or its prolongation by a circle, and point out how this type of situations come up in the quantization of Yang-Mills theory. 

  • 234. Mickelsson, Jouko
    Gerbes, (twisted) K-theory, and the supersymmetric WZW model2004In: Infinite dimensional groups and manifolds, Berlin: de Gruyter, Berlin , 2004, p. 93-1007Conference paper (Refereed)
  • 235.
    Mickelsson, Jouko
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Star products and central extensions2006In: Analysis, geometry and topology of elliptic operators / [ed] Bernhelm Booss-Bavnbek, Hackensack, NJ: World Scientific Publ. , 2006, p. 401-410Conference paper (Refereed)
  • 236.
    Milani, Sina
    et al.
    RMIT Univ, Sch Engn, Melbourne, Vic, Australia..
    Momtaz, Aidin
    Isfahan Univ Technol, Dept Phys, Esfahan, Iran..
    Amini, Sarah
    KN Toosi Univ Technol, Dept Comp Engn, Tehran, Iran..
    Amini, Kasra
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Sadeghi, Shekoufeh
    KN Toosi Univ Technol, Dept Comp Engn, Tehran, Iran..
    Qoreishi, Ehsan
    Isfahan Univ Technol, Dept Phys, Esfahan, Iran..
    Haddadian, Sanaz
    Univ Paderborn, Heinz Nixdorf Inst, Syst & Circuit Technol Grp, Paderborn, Germany..
    A Mathematical Approach Towards Random Road Profile Generation Based on Chaotic Signals of Chua's Circuit2022In: Contemporary Mathematics, ISSN 2705-1064, Vol. 3, no 1, p. 34-59Article in journal (Refereed)
    Abstract [en]

    In response to application demands in vehicle dynamics and control, traffic engineering, urban planning, and logistics, the generation of an adequate artificial road profile in terms of the diversity of geometric scenarios has been addressed in the current manuscript. The underlying mathematical principles for generating a geometrically comprehensive, yet logically meaningful, 3D road profile have been taken from high and unbiased sweeping factors of random number sequences over their domain of interest. And to generate such random number sequences, the mathematically manipulated output signal of a well-established chaotic system has been utilized, namely that of the Chua's circuit. Having defined the target road profile mathematically with all its geometrical complexities, a suitable scheme derived from the mentioned chaotic signal has been used to generate the required random number sequences as defining parameters of the road profile. The scheme has been otherwise tested and proven to show the demanded level of randomness in literature. Several attempts have been made to create a diverse range of road profiles. considering the constraints imposed by vehicle dynamics. To generate the road geometries, the limitations imposed by the vehicle's motion, such as the limitations on corresponding curvatures, slopes, and banking angles are negotiated, in terms of vehicle dynamics and available tire-road friction forces, by evaluating how close a vehicle will be to its tire force capacity limits as it travels on sections of the generated road.

  • 237.
    Molén, Ricky
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Branching Out with Mixtures: Phylogenetic Inference That’s Not Afraid of a Little Uncertainty2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Phylogeny, the study of evolutionary relationships among species and other taxa, plays a crucial role in understanding the history of life. Bayesian analysis using Markov chain Monte Carlo (MCMC) is a widely used approach for inferring phylogenetic trees, but it suffers from slow convergence in higher dimensions and is slow to converge. This thesis focuses on exploring variational inference (VI), a methodology that is believed to lead to improved speed and accuracy of phylogenetic models. However, VI models are known to concentrate the density of the learned approximation in high-likelihood areas. This thesis evaluates the current state of Variational Inference Bayesian Phylogenetics (VBPI) and proposes a solution using a mixture of components to improve the VBPI method's performance on complex datasets and multimodal latent spaces. Additionally, we cover the basics of phylogenetics to provide a comprehensive understanding of the field.

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  • 238. Motamed, M.
    et al.
    Runborg, Olof
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    A wavefront-based Gaussian beam method for computing high frequency wave propagation problems2015In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 69, no 9, p. 949-963Article in journal (Refereed)
    Abstract [en]

    We present a novel wavefront method based on Gaussian beams for computing high frequency wave propagation problems. Unlike standard geometrical optics, Gaussian beams compute the correct solution of the wave field also at caustics. The method tracks a front of two canonical beams with two particular initial values for width and curvature. In a fast post-processing step, from the canonical solutions we recreate any other Gaussian beam with arbitrary initial data on the initial front. This provides a simple mechanism to include a variety of optimization processes, including error minimization and beam width minimization, for a posteriori selection of optimal beam initial parameters. The performance of the method is illustrated with two numerical examples.

  • 239.
    Moustaid, Elhabib
    et al.
    KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Biomedical Engineering and Health Systems, Health Informatics and Logistics.
    Flötteröd, Gunnar
    KTH, School of Architecture and the Built Environment (ABE).
    Macroscopic Modelling of Complex Multidirectional Pedestrian IntersectionsManuscript (preprint) (Other academic)
    Abstract [en]

    Pedestrian movements are complex to understand and predict. The study of pedestrian flows is useful to the design and operation of pedestrian spaces. This article describes an approach to macroscopically model flows at multidirectional pedestrian intersec- tions. The proposed model relies on an existing pedestrian bidirectional fundamental diagram in combination with the incremental transfer principles in urban intersections to find flows at the level of pedestrian interfaces and intersections as a function of den- sities and few measurable parameters. The model writes the multidirectional pedestrian flows as a system of equations of dependent unidirectional flows. The final model is used as a cell transmission model, and it exhibits behaviour consistent with the Kine- matic Wave Model. The model allows simulating large pedestrian networks over time, relying on very few measurable parameters.

  • 240.
    Murray, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On Modelling Ancillary Services Markets: A Time Series Approach2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    So-called ancillary services (AS) have always been critically important for the functioning of an electrical grid, and are becoming even more so with the advent of renewable energy sources.

    Ancillary services are traded on open markets, and trading on these markets is arguably even more difficult to model than on traditional markets. This is, among other things, due to the limited availability of information such as current price, trading volume, etc., information that is typically available to traders on traditional markets. The goal of this thesis is to investigate whether the mean price of contracts on the FCR-D market (one of the AS markets) can be predicted with any useful accuracy using time series models, despite this scarcity of information.

    Utilizing hourly mean price data ranging from the present moment to several years in the past, different specifications of ARIMA models are fitted to the data and their performance compared. The performance of these models' predictions are found to only barely outperform a naïve approach. The reasons for why this may be the case are investigated and discussed, and potential improvements utilizing approaches such as GARCH and trigonometric representations of seasonal components are presented. This thesis does not, however, present any conclusive evidence for or against the suitability of ARIMA models for forecasting the FCR-D market, nor does it investigate alternatives in detail.

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  • 241.
    Möller, Andreas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Zero Coupon Yield Curve Construction Methods in the European Markets2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this study, four frequently used yield curve construction methods are evaulated on a set of metrics with the aim of determining which method is the most suitable for estimating yield curves from European zero rates. The included curve construction methods are Nelson-Siegel, Nelson-Siegel-Svensson, cubic spline interpolation and forward monotone convex spline interpolation. We let the methods construct yield curves on multiple sets of zero yields with different origins. It is found that while the interpolation methods show greater ability to adapt to variable market conditions as well as hedge arbitrary fixed income claims, they are outperformed by the parametric methods regarding the smoothness of the resulting yield curve as well as their sensitivity to noise and perturbations in the input rates. This apart from the Nelson-Siegel method's problem of capturing the behavior of underlying rates with a high curvature. The Nelson-Siegel-Svensson method did also exhibit instability issues when exposed to perturbations in the input rates. The Nelson-Siegel method and the forward monotone convex spline interpolation method emerge as most favorable in their respective categories. The ultimate selection between the two methods must however take the application at hand into consideration due to their fundamentally different characteristics.

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  • 242.
    Naim, Omar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Pricing Complex derivatives under the Heston model2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The calibration of model parameters is a crucial step in the process of valuation of complex derivatives. It consists of choosing the model parameters that correspond to the implied market data especially the call and put prices.

    We discuss in this thesis the calibration strategy for the Heston model, one of the most used stochastic volatility models for pricing complex derivatives. The main problem with this model is that the asset price does not have a known probability distribution function. Thus we use either Fourier expansions through its characteristic function or Monte Carlo simulations to have access to it. We hence discuss the approximation induced by these methods and elaborate a calibration strategy with a focus on the choice of the objective function and the choice of inputs for the calibration.

    We assess that the put option prices are a better input than the call prices for the optimization function. Then through a set of experiments on simulated put prices, we find that the sum of squared error performs better choice of the objective function for the differential evolution optimization. We also establish that the put option prices where the Black Scholes delta is equal to 10\%, 25\%, 50\% 75\% and 90\% gives enough in formations on the implied volatility surface for the calibration of the Heston model. We then implement this calibration strategy on real market data of Eurostoxx50 Index and observe the same distribution of errors as in the set of experiments.

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  • 243.
    Neander, Benjamin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Mattson, Victor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    An Attempt at Pricing Zero-Coupon Bonds under the Vasicek Model with a Mean Reverting Stochastic Volatility Factor2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Empirical evidence indicates that the volatility in asset prices is not constant, but varies over time. However, many simple models for asset pricing rest on an assumption of constancy. In this thesis we analyse the zero-coupon bond price under a two-factor Vasicek model, where both the short rate and its volatility follow Ornstein-Uhlenbeck processes. Yield curves based on the two-factor model are then compared to those obtained from the standard Vasicek model with constant volatility. The simulated yield curves from the two-factor model exhibit "humps" that can be observed in the market, but which cannot be obtained from the standard model.

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  • 244.
    Nieto, Stephan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Identifying Optimal Throw-in Strategy in Football Using Logistic Regression2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Set-pieces such as free-kicks and corners have been thoroughly examined in studies related to football analytics in recent years. However, little focus has been put on the most frequently occurring set-piece: the throw-in. This project aims to investigate how football teams can optimize their throw-in tactics in order to improve the chance of taking a successful throw-in. Two different definitions of what constitutes a successful throw-in are considered, firstly if the ball is kept in possession and secondly if a goal chance is created after the throw-in. The analysis is conducted using logistic regression, as this model comes with high interpretability, making it easier for players and coaches to gain direct insights from the results. A substantial focus is put on the investigation of the logistic regression assumptions, with the greatest emphasis being put on the linearity assumption. The results suggest that long throws directed towards the opposition’s goal are the most effective for creating goal-scoring opportunities from throw-ins taken in the attacking third of the pitch. However, if the throw-in is taken in the middle or defensive regions of the pitch, the results interestingly indicate that throwing the ball backwards leads to increased chance of scoring. When it comes to retaining the ball possession, the results suggest that throwing the ball backwards is an effective strategy regardless of the pitch position. Moreover, the project outlines how feature transformations can be used to improve the fitting of the logistic regression model. However, it turns out that the most significant improvement in accuracy of logistic regression occurs when incorporating additional relevant features into the model. In such case, the logistic regression model achieves a predictive power comparable to more advanced machine learning methods.

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  • 245.
    Niland, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sustainable Versus Non-Sustainable Equities: An Empirical Analysis of Return, Risk and Liquidity2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In order to create a sustainable portfolio, more sustainable assets may be chosen to be included and less sustainable assets may be chosen to be excluded from the portfolio. A potential risk that could arise as a result, is that the choice to include or exclude assets may affect the liquidity profile of the portfolio. For example if less liquid assets are included and more liquid assets are excluded. This thesis thus aims to investigate how the liquidity, but also other risks related to a stock portfolio, are related to the assets chosen to be included or excluded from the portfolio. 

    The main results obtained showed that the both the more and less sustainable assets on average had similar liquidity risk when considering the volume-based measure ILLIQ and the price-based measure MEC. The transaction cost-based measure the bid-ask spread, showed that the more sustainable assets had a significantly lower spread than the less sustainable, indicating that the market has a harder time agreeing on a fair price for these assets. The more sustainable assets also had a lower risk of potential losses compared to both the less sustainable and the market as a whole when considering the weekly returns, and also performed better over the considered time period. However, the less sustainable assets were shown to be slightly less volatile compared to the other assets.

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  • 246.
    Nordin Gröning, Jacob
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Minimal Cantor sets2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    A Cantor set is a topological space which admits a hierarchy of clopen covers. A minimal Cantor set is a Cantor set together with a map such that every orbit is dense in the Cantor set. In this thesis we us inverse limits to study minimal Cantor sets and their properties. In particular, under certain hypothesis we find an upper bound for the number of ergodic measures for minimal Cantor set.

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  • 247.
    Nord-Nilsson, William
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Generating Extreme Value Distributions in Finance using Generative Adversarial Networks2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis aims to develop a new model for stress-testing financial portfolios using Extreme Value Theory (EVT) and General Adversarial Networks (GANs). The current practice of risk management relies on mathematical or historical models, such as Value-at-Risk and expected shortfall. The problem with historical models is that the data which is available for very extreme events is limited, and therefore we need a method to interpolate and extrapolate beyond the available range. EVT is a statistical framework that analyzes extreme events in a distribution and allows such interpolation and extrapolation, and GANs are machine-learning techniques that generate synthetic data. The combination of these two areas can generate more realistic stress-testing scenarios to help financial institutions manage potential risks better. The goal of this thesis is to develop a new model that can handle complex dependencies and high-dimensional inputs with different kinds of assets such as stocks, indices, currencies, and commodities and can be used in parallel with traditional risk measurements. The evtGAN algorithm shows promising results and is able to mimic actual distributions, and is also able to extrapolate data outside the available data range.

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  • 248.
    Nordström, Christofer
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    DCC-GARCH Estimation2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    When modelling more that one asset, it is desirable to apply multivariate modeling to capture the co-movements of the underlying assets. The GARCH models has been proven to be successful when it comes to volatility forecast- ing. Hence it is natural to extend from a univariate GARCH model to a multivariate GARCH model when examining portfolio volatility. This study aims to evaluate a specific multivariate GARCH model, the DCC-GARCH model, which was developed by Engle and Sheppard in 2001. In this pa- per different DCC-GARCH models have been implemented, assuming both Gaussian and multivariate Student’s t distribution. These distributions are compared by a set of tests as well as Value at Risk backtesting.

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  • 249.
    Nordström, Oscar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Unstructured pruning of pre-trained language models tuned for sentiment classification.2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Transformer-based models are frequently used in natural language processing. These models are oftenlarge and pre-trained for general language understanding and then fine-tuned for a specific task. Becausethese models are large, they have a high memory requirement and have high inference time. Severalmodel compression techniques have been developed in order to reduce the mentioned disadvantageswithout significantly reducing the inference performance of the models. This thesis studies unstructuredpruning method, which are pruning methods that do not follow a predetermined pattern when removingparameters, to understand which parameters can be removed from language models and the impact ofremoving a significant portion of a model's parameters. Specifically, magnitude pruning, movementpruning, soft movement pruning, and $L_0$ regularization were applied to the pre-trained languagemodels BERT and M-BERT. The pre-trained models in turn were fine-tuned for sentiment classificationtasks, which refers to the task of classifying a given sentence to predetermined labels, such as positive ornegative. Magnitude pruning worked the best when pruning the models to a ratio of 15\% of the models'original parameters, while soft movement pruning worked the best for the weight ratio of 3\%. Formovement pruning, we were not able to achieve satisfying results for binary sentiment classification.From investigating the pruning patterns derived from soft movement pruning and $L_0$ regularization, itwas found that a large portion of the parameters from the last transformer blocks in the model architecturecould be removed without significantly reducing the model performance. An example of interestingfurther work is to remove the last transformer blocks altogether and investigate if an increase in inferencespeed is attained without significantly reducing the performance.

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  • 250.
    Norell, Simon
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Statistical Credit Rating with Survival Regression & Gradient Boosting2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis concerns the application of statistical modelling of credit risk in corporate borrowers using historical loan data from the Swedish export credit agency Exportkreditnämnden (EKN). Survival Regression in general and the Cox Proportional Hazard (CoxPH) model in particular is presented as a framework applicable to corpoate default and better suited than classification for modeling the binary default outcome of risk exposure data with inconsistent exposure times. This thesis focuses on a Gradient Boosting Machine application of the CoxPH model but uses the normal variant alongside for comparison. Partitioning the continous output of the model into discrete rating classes is explored as a method for making the results in a more intuitive fashion and make them comparable to credit risk modelling frameworks using non-parametric or non-statistical methods.

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