Displaying theses 110 of 424 total
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W.A. Martens 
Master programme: Stochastics and Financial Mathematics  September 25th, 2018  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: Peter Spreij 

Capital Valuation Adjustment In the wake of the 2008 ﬁnancial crisis, regulatory capital requirements for banks have increased signiﬁcantly through Basel III. As this raised awareness for the capital burden on the derivative businesses of banks, demand has grown for models that assess the costs of holding capital. Amidst a recent trend of pricing valuation adjustments, known as XVAs, a valuation adjustment has been developed that captures precisely this capital cost: the Capital Valuation Adjustment1. In this thesis, two approaches to modeling KVA are studied and compared. Although the models have diﬀerent mathematical fundamentals, the resulting KVA formulae are surprisingly similar. Both allow for Monte Carlo simulation of regulatory capital proﬁles to calculate KVA numbers. A computer implementation is considered, for both the existing and future regulatory landscape. 

Scientific abstract (pdf 104K) Full text (pdf 1581K) 
M.F. Perez Ortiz 
Master programme: Mathematics MSc  September 20th, 2018  
Institute: KdVI  Research group: Stochastics  Graduation thesis  Supervisor: Harry van Zanten 

Fast Rate Conditions in Statistical Learning Many problems in statistics, pattern recognition, and machine learning can be formulated in the following way. We want to choose a hypothesis from a hypotheses class based on data and we have a notion of what it means for a choice to be bad given a data point, encoded on a loss function. The goal is then to choose a hypothesis such that the expected loss for future observations is small. Examples of this include prototypical problems such as classification and regression. In these problems, hypotheses with a low expected loss are better at making predictions on future data. In this work we investigated how the expected loss of databased estimates of good hypotheses decreases to the lowest possible in the hypotheses class as the number of data points increases. It is known that under weak conditions this occurs in such a way that gathering ~10000 more data points results in an improvement of a factor of ~100. We considered conditions under which only ~100 times more data points would be needed to obtain the same result. These conditions are well known when losses are bounded; we investigated them in the unbounded case. 

Scientific abstract (pdf 1K) Full text (pdf 493K) 
S.P. Janse 
Master programme: Stochastics and Financial Mathematics  September 4th, 2018  
Institute: UvA / Other  Research group: Kortewegde Vries Institute for Mathematics  Graduation thesis  Supervisor: Sandjai Bhulai 

Optimizing Taxi Fleet Management Optimizing taxi fleet management has already been done via Markov decision processes. Recently, there has also been a taxi fleet management optimization using path covers in graph theory. This thesis will elaborate on both methods and can bring these solutions close to each other. First, an introduction in graph and flow theory is given. Second, we will elaborate on the graph interpretation which optimizes this problem. Third, the solution regarding the Markov decision theory is explained. Surprisingly, the two methods, which take place in two different fields, seem to both have a solution in the graph theory. 

Scientific abstract (pdf 1K) Full text (pdf 590K) 
J. Bajzelj 
Master programme: Stochastics and Financial Mathematics  August 30th, 2018  
Institute: UvA / Other  Research group: Kortewegde Vries Institute for Mathematics  Graduation thesis  Supervisor: Bert van Es 

Credit risk and survival analysis: Estimation of Conditional Cure Rate In this master thesis we looked into three estimators of Conditional Cure Rate (CCR). CCR estimation is done with survival analysis. CCR is used in the estimation of Loss Given Default (LGD). In credit risk LGD tells us the expected loss of the bank if its client defaults. After the default two events can happen, cure and liquidation. CCR tells use the probability that cure will happen strictly after time t conditioned on the event that client is still unresolved at time t. 

Scientific abstract (pdf 1K) Full text (pdf 1398K) 
C. Tioli 
Master programme: Stochastics and Financial Mathematics  August 29th, 2018  
Institute: UvA / Other  Research group: Kortewegde Vries Institute for Mathematics  Graduation thesis  Supervisor: Bas Kleijn 

Computational Aspects of Gaussian Process Regression Gaussian process regression is a useful and extremely powerful methodology which has been used in many fields, such as machine learning, classification, geostatistics and so on. It depends on parameters, called GPR hyperparameters which need to be estimated from training data. It is usually done by maximizing the marginal loglikelihood. A potential problem that one can encounter is the existence of multiple local maxima and therefore, the estimated hyperparameter may not be a global maximum. This thesis, in particular, focuses on a specific and simple GPR model which depends only on two hyperparameters. This work combines theoretical and numerical study of the marginal likelihood, as function of the hyperparameters. Firstly, its asymptotic behaviour is studied and properties regarding the more general function behaviour are derived. Then, we numerically study the function, implementing optimisation algorithms in order to find the local maxima, and locate the global maximum of the function. Moreover, we run simulations in order to estimate the probability of having one, two or more local optima. Finally, the main and most important goal of this thesis is to find an automatic and systematic method to detect a number of (and possibly all) the local maxima of the marginal likelihood. 

Scientific abstract (pdf 1K) Full text (pdf 2878K) 
S.P.H.M. Frerix 
Master programme: Stochastics and Financial Mathematics  August 21st, 2018  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: P.J.C. Spreij 
Efficient estimation of the Solvency Capital Requirement using Neural Networks In this thesis different models for estimating the Solvency Capital Requirement have been studied. The Solvency Capital Requirement is the amount of capital that insurers need to have available to cover a loss that is expected to occur once in every 200 years. Due to the complicated payoff structure of insurance liabilities the estimation of the capital requirement is a complex calculation. Even modern computers take many years to complete the entire calculation. This thesis explores proxy models based on neural networks to reduce the amount of time needed. The models proposed in this thesis are able to reduce computation time from years to days. 

Scientific abstract (pdf 1K) Full text (pdf 1554K) 
R.J. Mann 
Master programme: Mathematics MSc  August 7th, 2018  
Institute: KdVI  Research group: Algebraic Geometry  Graduation thesis  Supervisor: dr. A.L. Kret 
Images of Adelic Representations of Modular Forms A newform is a wellbehaved holomorphic function on the Poincaré plane that gives a number field, and a twodimensional Galois representation over the ring of finite adeles of that number field. In the "elliptic case", i.e. when the representation also come from representations of an elliptic curve without complex multiplication over the rational numbers, the representation was proven by JeanPierre Serre to have open image. However this is not true in general. In David Loeffler's paper, "Images of adelic Galois representations for modular forms", he was able to find a suitable way to generalise this result to all newforms without complex multiplication. 

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S.J. van den Brink 
Master programme: Mathematical Physics  July 30th, 2018  
Institute: KdVI  Research group: Mathematical Physics  Graduation thesis  Supervisor: dr. Raf Bocklandt 
Mapping class groups The mapping class group of a surface is the group of symmetries of that surface. The twofold torus for example has an obvious symmetry, namely ``interchanging the two tori''. Symmetries of an object are always certain maps from the object to itself. In this case we will be looking at bijective continuous maps from the surface to itself. However, we will only be looking at the ``really different symmetries'', where two symmetries are only ``really different'' if one cannot deform the first symmetry continuously into the second. It turns out that the maps that are not ``really different'' from the identity map, form a normal subgroup of the group of bijective continuous maps from the surface to itself. One can check easily that the classes of bijective continuous maps that are ``really the same'' are the cosets of this normal subgroup. So one defines the mapping class group to be the group of bijective continuous maps from the surface to itself, modulo the maps that are not ``really different'' from the identity. 

Scientific abstract (pdf 1K) For more info or full text, mail to: raf.bocklandt@gmail.com 
L.D. Stehouwer 
Master programme: Mathematical Physics  July 17th, 2018  
Institute: KdVI  Research group: Mathematical Physics  Graduation thesis  Supervisor: Hessel Posthuma 

Ktheory Classifications for SymmetryProtected Topological Phases of Free Fermions Topological insulators form a recently discovered class of materials with several interesting properties. During the 21st century, it has become clear that topological insulators can be classified using methods from algebraic topology, in particular Ktheory. In this thesis, a Ktheory framework is developed for classifying certain topological phases protected by a symmetry group. Computational methods are developed to compute the Ktheory groups and the computations are performed in basic examples. 

Scientific abstract (pdf 1K) Full text (pdf 955K) 
M.B. Blom 
Bachelor programme: Mathematics  July 13th, 2018  
Institute: KdVI  Research group: Algebraic Geometry  Graduation thesis  Supervisor: Lenny Taelman 

Dirichlet Lseries and transforming generators of principal ideals in latticebased cryptography We will discuss the principle of publickey cryptography, which is used when surfing the internet. In this case we have a person A trying to send a message to a person B. There is a third person E, who is trying to eavesdrop on the conversation. Person A encrypts a message using the public key, and sends the encrypted message to B. This encrypted message can only be decrypted using the secret key, so person E cannot see the contents of the message. When B receives the message, they can receive it using the secret key. Quantum computers can easily break encryption such as RSA. Even though current quantum computers are not powerful enough to actually break encryption, it is important to develop new futureproof cryptography. On of the possibilities is cryptography based on lattices. In this thesis we show an algorithm that breaks certain latticebased cryptography by computing the secret key. This allows anyone to decrypt encrypted message, showing that the encryption scheme is not secure. Furthermore, the mathematical background of cryptography is discussed, including algebraic number theory. Some more results from algebraic number theory are also discussed. 

Scientific abstract (pdf 1K) Full text (pdf 586K) 
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