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  • 1.
    Abbaszadeh Shahri, Abbas
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap.
    Larsson, Stefan
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap, Jord- och bergmekanik.
    Johansson, Fredrik
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap, Jord- och bergmekanik.
    Updated relations for the uniaxial compressive strength of marlstones based on P-wave velocity and point load index test2016Inngår i: INNOVATIVE INFRASTRUCTURE SOLUTIONS, ISSN 2364-4176, Vol. 1, nr 1, artikkel-id UNSP 17Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Although there are many proposed relations for different rock types to predict the uniaxial compressive strength (UCS) as a function of P-wave velocity (V-P) and point load index (Is), only a few of them are focused on marlstones. However, these studies have limitations in applicability since they are mainly based on local studies. In this paper, an attempt is therefore made to present updated relations for two previous proposed correlations for marlstones in Iran. The modification process is executed through multivariate regression analysis techniques using a provided comprehensive database for marlstones in Iran, including UCS, V-P and Is from publications and validated relevant sources comprising 119 datasets. The accuracy, appropriateness and applicability of the obtained modifications were tested by means of different statistical criteria and graph analyses. The conducted comparison between updated and previous proposed relations highlighted better applicability in the prediction of UCS using the updated correlations introduced in this study. However, the derived updated predictive models are dependent on rock types and test conditions, as they are in this study.

  • 2.
    Abdalmoaty, Mohamed
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Learning Stochastic Nonlinear Dynamical Systems Using Non-stationary Linear Predictors2017Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The estimation problem of stochastic nonlinear parametric models is recognized to be very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the maximum likelihood estimator and the optimal mean-square error predictor using Monte Carlo methods. Albeit asymptotically optimal, these methods come with several computational challenges and fundamental limitations.

    The contributions of this thesis can be divided into two main parts. In the first part, approximate solutions to the maximum likelihood problem are explored. Both analytical and numerical approaches, based on the expectation-maximization algorithm and the quasi-Newton algorithm, are considered. While analytic approximations are difficult to analyze, asymptotic guarantees can be established for methods based on Monte Carlo approximations. Yet, Monte Carlo methods come with their own computational difficulties; sampling in high-dimensional spaces requires an efficient proposal distribution to reduce the number of required samples to a reasonable value.

    In the second part, relatively simple prediction error method estimators are proposed. They are based on non-stationary one-step ahead predictors which are linear in the observed outputs, but are nonlinear in the (assumed known) input. These predictors rely only on the first two moments of the model and the computation of the likelihood function is not required. Consequently, the resulting estimators are defined via analytically tractable objective functions in several relevant cases. It is shown that, under mild assumptions, the estimators are consistent and asymptotically normal. In cases where the first two moments are analytically intractable due to the complexity of the model, it is possible to resort to vanilla Monte Carlo approximations. Several numerical examples demonstrate a good performance of the suggested estimators in several cases that are usually considered challenging.

  • 3.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lunz, Sebastian
    Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England..
    Banach Wasserstein GAN2018Inngår i: Advances in Neural Information Processing Systems 31 (NIPS 2018) / [ed] Bengio, S Wallach, H Larochelle, H Grauman, K CesaBianchi, N Garnett, R, Neural Information Processing Systems (NIPS) , 2018Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which induces a notion of distance between probability distributions of images. So far the community has considered l(2) as the underlying distance. We generalize the theory of WGAN with gradient penalty to Banach spaces, allowing practitioners to select the features to emphasize in the generator. We further discuss the effect of some particular choices of underlying norms, focusing on Sobolev norms. Finally, we demonstrate a boost in performance for an appropriate choice of norm on CIFAR-10 and CelebA.

  • 4.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Box 7593, 103 93 Stockholm, Sweden.
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Learning to solve inverse problems using Wasserstein lossManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.

  • 5.
    Agering, Harald
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    True risk of illiquid investments2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Alternative assets are becoming a considerable portion of global financial markets. Some of these alternative assets are highly illiquid, and as such they may require more intricate methods for calculating risk and performance statistics accurately. Research on hedge funds has established a pattern of risk being understated and various measures of performance being overstated due to illiquidity of the assets. This paper sets out to prove the existence of such bias and presents methods for removing it. Four mathematical methods aiming to adjust statistics for sparse return series were considered, and an implementation was carried out for data on private equity, real estate and infrastructure assets. The results indicate that there are in general substantial adjustments made to the risk and performance statistics of the illiquid assets when using these methods. In particular, the volatility and market exposure were adjusted upwards while manager skill and risk-adjusted performance were adjusted downwards.

  • 6.
    Ahlberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Application of the Ordered Lorenz Curve in the Analysis of a Non-Life Insurance Portfolio2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Insurance analysts have a great variety of assessment tools at their disposal in order to ensure a healthy insurance portfolio. To describe the financial income and loss distribution of the insurance portfolio one of the more fundamental mathematical instrument is the Lorenz curve. A measure developed in the early 19th centrury by Max O. Lorenz which intended to describe a population’s income distribution in a macro perspective. By developing further on this method with guidance from the article by Frees, Meyers and Cummings, [5], a link between the Lorenz curve and the insurance portfolio’s risk segment will be investigated.

    By constructing an insurance rating function which determine an insurance expected loss, depending on the policyholders characteristics, ordering the premium and loss distributions by its relative loss the intent is to identify profitable blocks along the ordered Lorenz curve. With this insight an analyst can redefine the portfolio structure and highlight the desirable characteristics which define a policyholder. In order to keep up with the competition an insurer has to, in the long run, create a sustainable, profitable portfolio with lowering the risk of occurring greater insurance claims.

  • 7.
    Ahlgren, Marcus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Claims Reserving using Gradient Boosting and Generalized Linear Models2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    One fundamental function of an insurance company revolves around calculating the expected claims costs for which the insurer has to compensate its policyholders for. This is the process of claims reserving which is practised by actuaries using statistical methods. Over the last few decades statistical learning methods have become increasingly popular due to their ability to find complex patterns in any type of data. However, they have not been widely adapted within the insurance sector. In this thesis we evaluate the capability of claims reserving with the method of gradient boosting, a non-parametric statistical learning method that has proven to be successful within multiple other disciplines which has made it very popular. The gradient boosting technique is compared with the generalized linear model(GLM) which is widely used for modelling claims. We compare the models by using a claims data set provided by Länsförsäkringar AB which allows us to train the models and evaluate their performance on data not yet seen by the models. The models were implemented using R. The results show that the GLM has a lower prediction error. Also, the gradient boosting method requires more fine tuning to handle claims data properly while the GLM already possesses certain features that makes it suitable for claims reserving without making as many adjustments in the model implementation. The advantage of capturing complex dependencies in data is not fully utilized in this thesis since we only work with 6 predictor variables. It is more likely that gradient boosting can compete with GLM when predicting more complicated claims.

  • 8.
    Ahlgren, Markus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Internal Market Risk Modelling for Power Trading Companies2015Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Since the financial crisis of 2008, the risk awareness has increased in the -financial sector. Companies are regulated with regards to risk exposure. These regulations are driven by the Basel Committee that formulates broad supervisory standards, guidelines and recommends statements of best practice in banking supervision. In these regulations companies are regulated with own funds requirements for market risks.

    This thesis constructs an internal model for risk management that, according to the "Capital Requirements Regulation" (CRR) respectively the "Fundamental Review of the Trading Book" (FRTB), computes the regulatory capital requirements for market risks. The capital requirements according to CRR and FRTB are compared to show how the suggested move to an expected shortfall (ES) based model in FRTB will affect the capital requirements. All computations are performed with data that have been provided from a power trading company to make the results fit reality. In the results, when comparing the risk capital requirements according to CRR and FRTB for a power portfolio with only linear assets, it shows that the risk capital is higher using the value-at-risk (VaR) based model. This study shows that the changes in risk capital mainly depend on the different methods of calculating the risk capital according to CRR and FRTB respectively and minor on the change of risk measure.

  • 9.
    Ahmed, Ilyas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Importance Sampling for Least-Square Monte Carlo Methods2016Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Pricing American style options is challenging due to early exercise opportunities. The conditional expectation in the Snell envelope, known as the continuation value is approximated by basis functions in the Least-Square Monte Carlo-algorithm, giving robust estimation for the options price. By change of measure in the underlying Geometric Brownain motion using Importance Sampling, the variance of the option price can be reduced up to 9 times. Finding the optimal estimator that gives the minimal variance requires careful consideration on the reference price without adding bias in the estimator. A stochastic algorithm is used to find the optimal drift that minimizes the second moment in the expression of the variance after change of measure. The usage of Importance Sampling shows significant variance reduction in comparison with the standard Least-Square Monte Carlo. However, Importance Sampling method may be a better alternative for more complex instruments with early exercise opportunity.

  • 10.
    Ainomae, Ahti
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Teknisk informationsvetenskap.
    Bengtsson, Mats
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Teknisk informationsvetenskap.
    Trump, Tonu
    Tallinn Univ Technol, Dept Radio & Telecommun Engn, EE-12616 Tallinn, Estonia..
    Distributed Largest Eigenvalue-Based Spectrum Sensing Using Diffusion LMS2018Inngår i: IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, ISSN 2373-776X, Vol. 4, nr 2, s. 362-377Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we propose a distributed detection scheme for cognitive radio (CR) networks, based on the largest eigenvalues (LEs) of adaptively estimated correlation matrices (CMs), assuming that the primary user signal is temporally correlated. The proposed algorithm is fully distributed, there by avoiding the potential single point of failure that a fusion center would imply. Different forms of diffusion least mean square algorithms are used for estimating and averaging the CMs over the CR network for the LE detection and the resulting estimation performance is analyzed using a common framework. In order to obtain analytic results on the detection performance, the exact distribution of the CM estimates are approximated by a Wishart distribution, by matching the moments. The theoretical findings are verified through simulations.

  • 11.
    Ali, Dana
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Kap, Goran
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Statistical Analysis of Computer Network Security2013Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    In this thesis it isshown how to measure the annual loss expectancy of computer networks due to therisk of cyber attacks. With the development of metrics for measuring theexploitation difficulty of identified software vulnerabilities, it is possibleto make a measurement of the annual loss expectancy for computer networks usingBayesian networks. To enable the computations, computer net-work vulnerabilitydata in the form of vulnerability model descriptions, vulnerable dataconnectivity relations and intrusion detection system measurements aretransformed into vector based numerical form. This data is then used to generatea probabilistic attack graph which is a Bayesian network of an attack graph.The probabilistic attack graph forms the basis for computing the annualizedloss expectancy of a computer network. Further, it is shown how to compute anoptimized order of vulnerability patching to mitigate the annual lossexpectancy. An example of computation of the annual loss expectancy is providedfor a small invented example network

  • 12. Alm, Sven Erick
    et al.
    Janson, Svante
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    First critical probability for a problem on random orientations in G(n,p)2014Inngår i: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 19, s. 69-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the random graph G (n,p) with a random orientation. For three fixed vertices s, a, b in G(n,p) we study the correlation of the events {a -> s} (there exists a directed path from a to s) and {s -> b}. We prove that asymptotically the correlation is negative for small p, p < C-1/n, where C-1 approximate to 0.3617, positive for C-1/n < p < 2/n and up to p = p(2)(n). Computer aided computations suggest that p(2)(n) = C-2/n, with C-2 approximate to 7.5. We conjecture that the correlation then stays negative for p up to the previously known zero at 1/2; for larger p it is positive.

  • 13.
    Almgren, Lars
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Evaluation of HYDRA - A risk model for hydropower plants2016Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Vattenfall Hydro AB has more than 50 large scale power plants. In these power plants there are over 130 power generating units. The planning of renewals of these units is important to minimize the risk of having big breakdowns which inflict long downtime. Because all power plants are different Vattenfall Hydro AB started using a self developed risk model in 2003 to improve the comparisons between power plants. Since then the model has been used without larger improvements or validation.

    The purpose of this study is to evaluate and analyse how well the risk model has performed and is performing. This thesis is divided into five subsections where analyses are made on the input to the model, adverse events used in the model, the probabilities used in the model, risk forecasts from the model and finally trends for the periods the model has been used. In each subsection different statistical methods are used for the analyses.

    From the analyses it is clear that the low number of adverse events in power plants makes the usage of statistical methods for evaluating performance of Vattenfall Hydro AB’s risk model imprecise. Based on the results of this thesis the conclusion is made that if the risk model is to be used in the future it needs further improvements to generate more accurate results.

  • 14. Ameur, Yacin
    et al.
    Hedenmalm, Håkan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Makarov, Nikolai
    Random normal matrices and ward identities2015Inngår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 43, nr 3, s. 1157-1201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the correction to the expectation of the fluctuations, and we show that the potential field of the corrected fluctuations converge on smooth test functions to a Gaussian free field with free boundary conditions on the droplet associated with the potential.

  • 15.
    Amsköld, Daniel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    A comparison between different volatility models2011Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
  • 16.
    Andersson, Alexandra
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Smart Beta Investering Baserad på Makroekonomiska Indikatorer2015Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    This thesis examines the possibility to find a relationship between the Nasdaq Nordea Smart Beta Indices and a series of macroeconomic indicators. This relationship will be used as a signal-value and implemented in a portfolio consisting of all six smart beta indices. To investigate the impact of the signal-value on the portfolio performance, three portfolio strategies are examined with the equally weighted portfolio as a benchmark. The portfolio weights will be re-evaluated monthly and the portfolios examined are the mean-variance portfolio, the mean-variance portfolio based on the signal-value and the equally weighted portfolio based on the signal-value.

    In order to forecast the performance of the portfolio, a multivariate GARCH model with time-varying correlations is fitted to the data and three different error-distributions are considered. The performances of the portfolios are studied both in- and out-of-sample and the analysis is based on the Sharpe ratio.

    The results indicate that a mean-variance portfolio based on the relationship with the macroeconomic indicators outperforms the other portfolios for the in-sample period, with respect to the Sharpe ratio. In the out-of-sample period however, none of the portfolio strategies has Sharpe ratios that are statistically different from that of an equally weighted portfolio.

  • 17.
    Andersson, Daniel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    A mixed relaxed singular maximum principle for linear SDEs with random coefficientsArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a global form. A motivating example is given in the form of an optimal investment and consumption problem with transaction costs, where we consider a portfolio with a continuum of bonds and where the portfolio weights are modeled as measure-valued processes on the set of times to maturity.

  • 18.
    Andersson, Daniel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Contributions to the Stochastic Maximum Principle2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis consists of four papers treating the maximum principle for stochastic control problems.

    In the first paper we study the optimal control of a class of stochastic differential equations (SDEs) of mean-field type, where the coefficients are allowed to depend on the law of the process. Moreover, the cost functional of the control problem may also depend on the law of the process. Necessary and sufficient conditions for optimality are derived in the form of a maximum principle, which is also applied to solve the mean-variance portfolio problem.

    In the second paper, we study the problem of controlling a linear SDE where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditons for optimality in the form of a maximum principle, extended to include the family of relaxed controls.

    The third paper generalizes the second one by adding a singular control process to the SDE. That is, the control is singular with respect to the Lebesgue measure and its influence on the state is thus not continuous in time. In terms of the portfolio problem, this allows us to consider two investment possibilities - bonds (with a continuum of maturities) and stocks - and incur transaction costs between the two accounts.

    In the fourth paper we consider a general singular control problem. The absolutely continuous part of the control is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.

  • 19.
    Andersson, Daniel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Necessary Optimality Conditions for Two Stochastic Control Problems2008Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis consists of two papers concerning necessary conditions in stochastic control problems. In the first paper, we study the problem of controlling a linear stochastic differential equation (SDE) where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditions for optimality in the form of a maximum principle, extended to include the family of relaxed controls.

    In the second paper we consider the so-called singular control problem where the control consists of two components, one absolutely continuous and one singular. The absolutely continuous part of the control is allowed to enter both the drift and diffusion coefficient. The absolutely continuous part is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.

  • 20.
    Andersson, Daniel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    The relaxed general maximum principle for singular optimal control of diffusions2009Inngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, ISSN 01676911, Vol. 58, nr 1, s. 76-82Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study optimality in stochastic control problems where the state process is a stochastic differential equation (SDE) and the control variable has two components, the first being absolutely continuous and the second singular. A control is defined as a solution to the corresponding martingale problem. To obtain existence of an optimal control Haussmann and Suo [U.G. Haussmann, W. Suo, Singular optimal stochastic controls I: Existence, SIAM J. Control Optim. 33 (3) (1995) 916-936] relaxed the martingale problem by extending the absolutely continuous control to the space of probability measures on the control set. Bahlali et al. [S. Bahlali, B. Djehiche, B. Mezerdi, The relaxed stochastic maximum principle in singular optimal control of diffusions, SIAM J. Control Optim. 46 (2) (2007) 427-444] established a maximum principle for relaxed singular control problems with uncontrolled diffusion coefficient. The main goal of this paper is to extend their results to the case where the control enters the diffusion coefficient. The proof is based on necessary conditions for near optimality of a sequence of ordinary controls which approximate the optimal relaxed control. The necessary conditions for near optimality are obtained by Ekeland's variational principle and the general maximum principle for (strict) singular control problems obtained in Bahlali and Mezerdi [S. Bahlali, B. Mezerdi, A general stochastic maximum principle for singular control problems, Electron J. Probab. 10 (2005) 988-1004. Paper no 30]. © 2008 Elsevier B.V. All rights reserved.

  • 21.
    Andersson, Daniel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    The relaxed stochastic maximum principle in singular optimal control of diffusions with controlled diffusion coefficientManuskript (Annet vitenskapelig)
  • 22.
    Andersson, Daniel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization2010Inngår i: Mathematical Methods of Operations Research, ISSN 1432-2994, E-ISSN 1432-5217, Vol. 72, nr 2, s. 273-310Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a relaxed maximum principle. The main motivation is an optimal bond portfolio problem in a market where there exists a continuum of bonds and the portfolio weights are modeled as measure-valued processes on the set of times to maturity.

  • 23.
    Andersson, Daniel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    A maximum principle for SDEs of mean-field type2011Inngår i: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 63, nr 3, s. 341-356Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.

  • 24.
    Andersson, Gabriella
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Karlsson, Louise
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Factors affecting the proportion of smartphone usage at Flygresor.se2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    Digitization has changed the way people access the internet. Smartphones is soon to be the preferred internet access device leading us into a new generation of e-commerce, namely mobile commerce or m-commerce. The on-going transition, from desktop to smartphone has led to an uprising problem for companies within the area of e-commerce. Visitors coming from a smartphone device tend to not go through with the purchase. With this transition in mind, the thesis aimed to identify the factors that affect the proportion of smartphone visitors on a website, more specifically at the flight comparison site Flygresor.se. The method used was multiple linear regression analysis. To see whether the chosen factors affected the proportion of smartphone transactions or just the proportion of smartphone sessions two regression were performed. One with response variable Sessions and one with response variable Transactions, where Sessions refer to the number of visitors on the website and Transactions refer to the number of visitors moving on to the final booking website. The explanatory variables used were divided into four categories; Marketing, Channels, Season and Other, where the category Other contained the variables Total number of visitors and Amount of MB used per smartphone subscription. The study showed that all categories contained variables with significant impact on both of the response variables. There was only one variable that had different impact on the models, namely the Total number of visitors. The result indicates that smartphone users tend to, in comparison with desktop users, to a less extent continue to the final booking website. Since there were no other variables that only had an impact on Transactions it was assumed that there exist other factors which have a greater impact on smartphone users tendency to finalize a booking.

  • 25.
    Andersson, Joacim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Falk, Henrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Missing Data in Value-at-Risk Analysis: Conditional Imputation in Optimal Portfolios Using Regression2013Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    A regression-based method is presented in order toregenerate missing data points in stock return time series. The method usesonly complete time series of assets in optimal portfolios, in which the returnsof the underlying tend to correlate inadequately with each other. The studyshows that the method is able to replicate empirical VaR-backtesting resultswhere all data are available, even when up to 90% of the time series in half ofthe assets in the portfolios have been removed.

  • 26.
    Andersson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Locating Multiple Change-Points Using a Combination of Methods2014Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The aim of this study is to find a method that is able to locate multiple change-points in a time series with unknown properties. The methods that are investigated are the CUSUM and CUSUM of squares test, the CUSUM test with OLS residuals, the Mann-Whitney test and Quandt’s log likelihood ratio. Since all methods are detecting single change-points, the binary segmentation technique is used to find multiple change-points. The study shows that the CUSUM test with OLS residuals, Mann-Whitney test and Quandt’s log likelihood ratio work well on most samples while the CUSUM and CUSUM of squares are not able to detect the location of the change-points. Furthermore the study shows that the binary segmentation technique works well with all methods and is able to detect multiple change-points in most circumstances. The study also shows that the results can, most of the time, be improved by using a combination of the methods.

  • 27.
    Andersson, Markus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Multivariate Financial Time Series and Volatility Models with Applications to Tactical Asset Allocation2015Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The financial markets have a complex structure and the modelling techniques have recently been more and more complicated. So for a portfolio manager it is very important to find better and more sophisticated modelling techniques especially after the 2007-2008 banking crisis. The idea in this thesis is to find the connection between the components in macroeconomic environment and portfolios consisting of assets from OMX Stockholm 30 and use these relationships to perform Tactical Asset Allocation (TAA). The more specific aim of the project is to prove that dynamic modelling techniques outperform static models in portfolio theory.

  • 28.
    Andersson, Sofia
    et al.
    AstraZeneca R and D.
    Rydén, Tobias
    Lund University.
    Subspace estimation and prediction methods for hidden Markov models2009Inngår i: Annals of Statistics, ISSN 0090-5364, E-ISSN 2168-8966, Vol. 37, nr 6B, s. 4131-4152Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite set as well. In particular, we study the geometric structure arising from the nonminimality of the linear state space representation of HMMs, and consistency of a subspace algorithm arising from a certain factorization of the singular value decomposition of the estimated linear prediction matrix, For this algorithm, we show that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation, and that the in-step linear predictor Computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear m-step predictor.

  • 29.
    Annink, Marit
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Larsson, Rebecca
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Introduction of the Academic Factor Quality Minus Junk to a Commercial Factor Model and its Effect on the Explanatory Power. An OLS Regression on Stock Returns2019Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    The ability to predict stock returns is an ability many wish to possess, and in an accurate way as possible. For many years there has been an interest in the field of factor models explaining the returns, with the aim to increase the explanatory power. This is however a complex business since the factors and their improvement of explanatory power need to be significant. Now and then, researchers come up with new significant factors that have a positive impact on models. AQR Capital Management is no exception to this, since they in 2013 presented the factor Quality Minus Junk, earning significant risk-adjusted returns. This bachelor thesis work within mathematical statistics and industrial engineering and management, aims to investigate whether or not the commercial multi-factor model used at the public pension fund Fjärde AP-fonden will be improved by adding the factor Quality Minus Junk, in the sense of explanatory power. The method used is mainly based on multiple linear regression and three three-year time periods are studied ranging from 2010 to 2018. The results from this thesis work show that the QMJ factor provides significant increases in explanatory power for one of three time periods, the most recent period 2016$-$2018. However, since the results are inconclusive further studies are needed in order to better understand how to interpret the results and whether or not to include the QMJ factor in the model.

  • 30.
    Antonsson, Hermina
    KTH, Skolan för industriell teknik och management (ITM).
    Macroeconomic factors in Probability of Default: A study applied to a Swedish credit portfolio2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Macroeconomic conditions can impact the payment capacity of individual mortgage holders' household loans. If the clients of a bank's retail credit portfolio experience deteriorating paymentcapacity it will reflect on the probability of default of the overall portfolio. With IFRS 9, banks are expected to sophisticate their calculations of expected credit loss, demanding forward-looking estimates of probability of default by incorporation of macroeconomic forecasts. Finding what macroeconomic factors have a statistical significant relationship to the actual default frequency of a portfolio can aid banks in estimating probability of default with reference to current and forecasted macroeconomic conditions.

    This study aims to explore the relationship between macroeconomic factors and the default frequency in a Swedish retail credit portfolio. The research is based on quantitative data analysis of historical default data, complemented by implications of the macroeconomic condition on the payment capacity of households from a theoretical perspective.

    Macroeconomic factors studied are the Swedish gross domestic product, house price index, reporate and unemployment rate. The supporting data consists of default data from Nordea's Swedishretail credit portfolio. The time period covers 2008-2015 and provides basis for analysis of a timeperiod with different conditions in the macroeconomy, including effects of the 2008 financial crisis. A multiple linear regression model is used as a method to suggest the relationship between themacroeconomic factors and the default frequency. The model coefficients are estimated with calculations of Ordinary Least Squares and the significance supported by statistical test.

    Results show that gross domestic product and repo rate are statistically significant macroeconomic variables in explaining changes in the default frequency and thus probability of default of a Swedish retail credit portfolio.

  • 31.
    Armerin, Fredrik
    KTH, Tidigare Institutioner, Matematik.
    Aspects of cash-flow valuation2004Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    This thesis consists of five papers. In the first two papers we consider a general approach to cash flow valuation, focusing on dynamic properties of the value of a stream of cash flows. The third paper discusses immunization theory, where old results are shown to hold in general deterministic models, but often fail to be true in stochastic models. In the fourth paper we comment on the connection between arbitrage opportunities and an immunized position. Finally, in the last paper we study coherent and convex measure of risk applied to portfolio optimization and insurance.

  • 32.
    Armerin, Fredrik
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Fastigheter och byggande, Bygg- och fastighetsekonomi.
    Hallgren, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Koski, Timo
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Forecasting Ranking in Harness Racing Using Probabilities Induced by Expected Positions2019Inngår i: Applied Artificial Intelligence, ISSN 0883-9514, E-ISSN 1087-6545, Vol. 33, nr 2, s. 171-189Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Ranked events are pivotal in many important AI-applications such as Question Answering and recommendations systems. This paper studies ranked events in the setting of harness racing. For each horse there exists a probability distribution over its possible rankings. In the paper, it is shown that a set of expected positions (and more generally, higher moments) for the horses induces this probability distribution. The main contribution of the paper is a method, which extracts this induced probability distribution from a set of expected positions. An algorithm is proposed where the extraction of the induced distribution is given by the estimated expectations. MATLAB code is provided for the methodology. This approach gives freedom to model the horses in many different ways without the restrictions imposed by for instance logistic regression. To illustrate this point, we employ a neural network and ordinary ridge regression. The method is applied to predicting the distribution of the finishing positions for horses in harness racing. It outperforms both multinomial logistic regression and the market odds. The ease of use combined with fine results from the suggested approach constitutes a relevant addition to the increasingly important field of ranked events.

  • 33.
    Armerin, Fredrik
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Fastigheter och byggande.
    Han-Suck, Song
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Fastigheter och byggande.
    Valuation of real options in incomplete models – An implied yield approach2018Inngår i: Fuzzy Economic Review, ISSN 1136-0593, Vol. 23, nr 1, s. 19-32Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    In many applications of real options there is an assumption of complete capital markets. For the perpetual timing option this means that if the underlying asset does not pay out any cash flows, then there is no finite optimal time at which the investment should be undertaken. In contrast, when the market is incomplete there is a possibility of having a finite optimal stopping time even in the cases when the underlying asset does not pay out any cash flows. We discuss the incomplete case in models driven by both Brownian motion(s) and a Poisson process and connect it with the concept of an implied yield. The implied yield will in these models extend the concept of a monetary yield (i.e. a yield that represents the fraction of the value of an asset paid out as a cash flow). Several examples of incomplete market models where there could be a finite optimal time to invest are given.

  • 34. Aro, Helena
    et al.
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Löfdahl, Björn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Stochastic modelling of disability insurance in a multi-period framework2015Inngår i: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, nr 1, s. 88-106Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data.

  • 35. Asmussen, Sören
    et al.
    Rydén, Tobias
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    A Note on Skewness in Regenerative Simulation2011Inngår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 40, nr 1, s. 45-57Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this article is to show, empirically and theoretically, that performance evaluation by means of regenerative simulation often involves random variables with distributions that are heavy tailed and heavily skewed. This, in turn, leads to the variance of estimators being poorly estimated, and confidence intervals having actual coverage quite different from (typically lower than) the nominal one. We illustrate these general ideas by estimating the mean occupancy and tail probabilities in M/G/1 queues, comparing confidence intervals computed from batch means to various intervals computed from regenerative cycles. In addition, we provide theoretical results on skewness to support the empirical findings.

  • 36.
    Aurell, Alexander
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations2018Inngår i: Games, ISSN 2073-4336, E-ISSN 2073-4336, Vol. 9, nr 5Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 37.
    Aurell, Alexander
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Topics in the mean-field type approach to pedestrian crowd modeling and conventions2019Doktoravhandling, med artikler (Annet vitenskapelig)
    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.

  • 38.
    Aurell, Alexander
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Behavior near walls in the mean-field approach to crowd dynamicsManuskript (preprint) (Annet vitenskapelig)
  • 39.
    Aurell, Erik
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsvetenskap och beräkningsteknik (CST). Depts of Information and Computer Science and Applied Physics, Aalto University, Finland.
    Del Ferraro, Gino
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsvetenskap och beräkningsteknik (CST).
    Causal analysis, Correlation-Response, and Dynamic cavity2016Inngår i: International Meeting on High-Dimensional Data-Driven Science (HD3-2015), Institute of Physics (IOP), 2016, artikkel-id 012002Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the stationary state of a non-equilibrium process effectively, which could then be taken an alternative starting point of causal analysis.

  • 40.
    Back, Alexander
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Keith, William
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Bayesian Neural Networks for Financial Asset Forecasting2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Neural networks are powerful tools for modelling complex non-linear mappings, but they often suffer from overfitting and provide no measures of uncertainty in their predictions. Bayesian techniques are proposed as a remedy to these problems, as these both regularize and provide an inherent measure of uncertainty from their posterior predictive distributions. By quantifying predictive uncertainty, we attempt to improve a systematic trading strategy by scaling positions with uncertainty. Exact Bayesian inference is often impossible, and approximate techniques must be used. For this task, this thesis compares dropout, variational inference and Markov chain Monte Carlo. We find that dropout and variational inference provide powerful regularization techniques, but their predictive uncertainties cannot improve a systematic trading strategy. Markov chain Monte Carlo provides powerful regularization as well as promising estimates of predictive uncertainty that are able to improve a systematic trading strategy. However, Markov chain Monte Carlo suffers from an extreme computational cost in the high-dimensional setting of neural networks.

  • 41.
    Baghchesara, Sherwin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Evaluating ESG Related Events' Significance for Oil Companies in Relation To Stock Price Changes2019Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    ESG risks, which stands for environmental, social, and governance, has in recent years exploded as a conversational topic. Including ESG efforts in company reports, and being transparent about operations is not as foreign as before. However, companies operating in controversial sectors and areas, known to have great environmental impact, face increased pressure to comply with the ESG values. One sector would be the oil sector, which is known as one of the most controversial sectors in regards to social and environmental issues. Disastrous events, such as spills and deaths following operations, have spread fast and sometimes hit hard on stock prices. The report will assess changes in stock prices in relation to changes in ESG-risk scores and ESG news for a selected number of companies, as well as a few macro variables. For this, a multiple regression analysis will be carried through. The thesis concludes in a model in which the ESG variables cannot explain overall stock movements; the variables that are shown statistically significant are mainly macro variables. However, certain stock movements that are marked as influential points by the model, which in this case all were rapid stock movements, seem to be reflected better on the changes of the ESG variables, which paves the way for further research.

  • 42.
    Baldvindsdottir, Ebba-Kristin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    On Constructing a Market Consistent Economic Scenario Generator2011Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
  • 43. Bao, Z.
    et al.
    Erdős, L.
    Schnelli, Kevin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Local Law of Addition of Random Matrices on Optimal Scale2017Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 349, nr 3, s. 947-990Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.

  • 44.
    Barr, Kajsa
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Pettersson, Hampus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Predicting and Explaining Customer Churn for an Audio/e-book Subscription Service using Statistical Analysis and Machine Learning2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The current technology shift has contributed to increased consumption of media and entertainment through various mobile devices, and especially through subscription based services. Storytel is a company offering a subscription based streaming service for audio and e-books, and has grown rapidly in the last couple of years. However, when operating in a competitive market, it is of great importance to understand the behavior and demands of the customer base. It has been shown that it is more profitable to retain existing customers than to acquire new ones, which is why a large focus should be directed towards preventing customers from leaving the service, that is preventing customer churn. One way to cope with this problem is by applying statistical analysis and machine learning in order to identify patterns and customer behavior in data. In this thesis, the models logistic regression and random forest are used with an aim to both predict and explain churn in early stages of a customer's subscription. The models are tested together with the feature selection methods Elastic Net, RFE and PCA, as well as with the oversampling method SMOTE. One main finding is that the best predictive model is obtained by using random forest together with RFE, producing a prediction score of 0.2427 and a recall score of 0.7699. The other main finding is that the explanatory model is given by logistic regression together with Elastic Net, where significant regression coefficient estimates can be used to explain patterns associated with churn and give useful findings from a business perspective.

  • 45.
    Barwary, Sara
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Abazari, Tina
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Preprocessing Data: A Study on Testing Transformations for Stationarity of Financial Data2019Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    In thesis within Industrial Economics and Applied Mathematics in cooperation with Svenska Handelsbanken given transformations was examined in order to assess their ability to make a given time series stationary. In addition, a parameter α belonging to each of the transformation formulas was to be decided. To do this an extensive study of previous research was conducted and two different tests of hypothesis where obtained to confirm output. A result was concluded where a value or interval for α was chosen for each transformation. Moreover, the first difference transformation is proven to have a positive effect on stationarity of financial data.

  • 46.
    Batres-Estrada, Bilberto
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Deep learning for multivariate financial time series2015Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Deep learning is a framework for training and modelling neural networks which recently have surpassed all conventional methods in many learning tasks, prominently image and voice recognition. This thesis uses deep learning algorithms to forecast financial data. The deep learning framework is used to train a neural network. The deep neural network is a Deep Belief Network (DBN) coupled to a Multilayer Perceptron (MLP). It is used to choose stocks to form portfolios. The portfolios have better returns than the median of the stocks forming the list. The stocks forming the S&P 500 are included in the study. The results obtained from the deep neural network are compared to benchmarks from a logistic regression network, a multilayer perceptron and a naive benchmark. The results obtained from the deep neural network are better and more stable than the benchmarks. The findings support that deep learning methods will find their way in finance due to their reliability and good performance.

  • 47.
    Bayer, Christian
    et al.
    Weierstrass Institute for Applied Analysis and Stochastics.
    Hoel, Håkon
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    von Schwerin, Erik
    King Abdullah University of Science and Technology.
    Tempone, Raul
    King Abdullah University of Science and Technology.
    On non-asymptotic optimal stopping criteria in Monte Carlo simulations2012Rapport (Annet vitenskapelig)
    Abstract [en]

    We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in numerical examples to perform more reliably and only slightly less efficiently than the second moment based stopping rule.

  • 48.
    Beffara, Vincent
    et al.
    Univ Grenoble Alpes, CNRS, Inst Fourier, F-38000 Grenoble, France..
    Chhita, Sunil
    Univ Durham, Dept Math Sci, Durham DH1 3LE, England..
    Johansson, Kurt
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Royal Inst Technol KTH, Dept Math, Linstedtsvagen 25, SE-10044 Stockholm, Sweden..
    AIRY POINT PROCESS AT THE LIQUID-GAS BOUNDARY2018Inngår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 46, nr 5, s. 2973-3013Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using the height function, we define a random measure in the two-periodic Aztec diamond designed to detect the long range correlations visible at the liquid-gas boundary. We prove that this random measure converges to the extended Airy point process. This indicates that, in a sense, the liquid-gas boundary should also be described by the Airy process.

  • 49. Bengtsson, Göran
    et al.
    Nilsson, Elna
    Rydén, Tobias
    Lund University.
    Wiktorsson, Magnus
    Irregular walks and loops combines in small-scale movement of a soil insect: implications for dispersal biology2004Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 231, nr 2, s. 299-306Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Analysis of small-scale movement patterns of animals we may help to understand and predict movement at a larger scale, such as dispersal, which is a key parameter in spatial population dynamics. We have chosen to study the movement of a soil-dwelling Collembola, Protaphorura armata, in an experimental system consisting of a clay surface with or without physical obstacles. A combination of video recordings, descriptive statistics, and walking simulations was used to evaluate the movement pattern. Individuals were found to link periods of irregular walk with those of looping in ahomogeneous environment as well as in one structured to heterogeneity by physical obstacles. The number of loops varied between 0 and 44 per hour from one individual to another and some individuals preferred to make loops by turning right and others by turning left. P. armata spent less time at the boundary of small obstacles compared to large, presumably because of a lower probability to track the steepness of the curvature as the individual walks along a highly curved surface. Food deprived P. armata had amore winding movement and made more circular loops than those that were well fed. The observed looping behaviour is interpreted in the context of systematic search strategies and compared with similar movement patterns found in other species.

  • 50.
    Berg, Edvin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Orrsveden, Magnus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    A regression analysis of the factors affecting the ticket price in thetravel industry2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    This bachelor thesis in applied mathematics and industrial engineering and management investigates which factors that affect the price of tickets in the travel industry. This has been done by performing different multiple linear regression analyses based on the theory from mathematical statistics and econometrics. The analyses has been made with data that has been provided by MTR Express, containing data of departures of 2016 for the main operators in the railway and airline industry. The route that has been analysed is Stockholm - Gothenburg since this is the route where MTR Express has established its business in the railway market in Sweden. The results of the linear regression analysis show that the variables "Days before departure" and the weekday of travel have the most significant impact on the prices for both train and flight tickets. The final models have an explanation

    degree of 50% for the railway and 51% for the airline industry. The results show many similarities and correlations between the railway and airline industries. Furthermore, some interesting differences between these subindustries appeared in the final regression models and these have been one of the aspects in the discussion. The conclusion of the thesis is that there are several different aspects affecting the price in the travel industry

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