Mathematics in Progress

Home   Artificial Intell.   Bio-exact   Chemistry   Computer Sci. BSc   Earth Sciences   Mathematics   Physics & Astr.   Science Educ.   Submit   Webmaster        
bachelors   masters   all  


Displaying theses 1-10 of 424 total
Previous  1  2  3  4  5  6  7  8  9  10  11  Next  Search:

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
photo of the author
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.
picture that illustrates the research done
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
photo of the author
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 data-based 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.
picture that illustrates the research done
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: Korteweg-de Vries Institute for Mathematics Graduation thesis Supervisor: Sandjai Bhulai
photo of the author
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.
picture that illustrates the research done
Scientific abstract (pdf 1K)   Full text (pdf 590K)

J. Bajzelj
Master programme: Stochastics and Financial Mathematics August 30th, 2018
Institute: UvA / Other Research group: Korteweg-de Vries Institute for Mathematics Graduation thesis Supervisor: Bert van Es
photo of the author
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.
picture that illustrates the research done
Scientific abstract (pdf 1K)   Full text (pdf 1398K)

C. Tioli
Master programme: Stochastics and Financial Mathematics August 29th, 2018
Institute: UvA / Other Research group: Korteweg-de Vries Institute for Mathematics Graduation thesis Supervisor: Bas Kleijn
photo of the author
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 log-likelihood. 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.
picture that illustrates the research done
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 pay-off 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.
picture that illustrates the research done
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 well-behaved holomorphic function on the Poincaré plane that gives a number field, and a two-dimensional 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 Jean-Pierre 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.
picture that illustrates the research done
Scientific abstract (pdf 1K)   Full text (pdf 505K)

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 two-fold 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.
picture that illustrates the research done
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
photo of the author
K-theory Classifications for Symmetry-Protected 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 K-theory. In this thesis, a K-theory framework is developed for classifying certain topological phases protected by a symmetry group. Computational methods are developed to compute the K-theory groups and the computations are performed in basic examples.
picture that illustrates the research done
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
photo of the author
Dirichlet L-series and transforming generators of principal ideals in lattice-based cryptography
We will discuss the principle of public-key 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 future-proof cryptography. On of the possibilities is cryptography based on lattices. In this thesis we show an algorithm that breaks certain lattice-based 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.
picture that illustrates the research done
Scientific abstract (pdf 1K)   Full text (pdf 586K)

Previous  1  2  3  4  5  6  7  8  9  10  11  Next  

This page is maintained by thesis@science.uva.nl