Mathematics in Progress

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Displaying theses 1-10 of 398 total
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J.J. Kerssens
Master programme: Mathematics MSc April 20th, 2018
Institute: KdVI Research group: Stochastics Graduation thesis Supervisor: Sonja Cox
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Fourier multiplier theorems
This thesis focusses on how Fourier multipliers preserve integrability properties. Different conditions on multipliers m to ensure that the Fourier multiplier (i.e., a convolution) maps L^p to L^p are studied, such as the conditions in the classical Mihlin and Hörmander multiplier theorems. A recent generalization by Hytönen of both the Mihlin multiplier theorem and the Hörmander multiplier theorem for Fourier multipliers is given which provides stronger results even in the scalar case. Hytönen initially studies multipliers on Besov spaces which appear naturally in his approach. The technical proof of the generalized multiplier theorem is explained in detail and its connection to the classical theorems is discussed.
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Scientific abstract (pdf 1K)   For more info or full text, mail to: s.g.cox@uva.nl

R.N. Kuipers
Master programme: Mathematics MSc April 5th, 2018
Institute: KdVI Research group: Stochastics Graduation thesis Supervisor: A.V. den Boer
Understanding the dynamics of citation networks through preferential attachment models
Since the 1960s, the analysis of citations in scientific articles has become a major scientific field of itself. This citation analysis is done on citation networks in which scientific articles are represented as vertices that are linked with directed edges from one vertex to another by citation. But what determines the growth of a citation network? And is there a mechanism that can capture the dynamics behind the evolution of a citation network? In this thesis an extension of the preferential attachment model is introduced. This model can explain the growth of complex networks through the rich-get-richer and fit-get-richer paradigm. This is the idea that at every time step when a new vertex is added to a network it is more likely to connect to already well-connected vertices and it is also more likely to connect to vertices that have a high fitness, i.e. scientific articles that are of a high quality. There are two parameters that determine the growth of such a network. We will see how we can estimate these parameters based on observing the growing network. This will serve as a starting point for modelling real-world citation networks.
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Scientific abstract (pdf 1K)   Full text (pdf 2263K)

W. Wang
Master programme: Stochastics and Financial Mathematics January 15th, 2018
Institute: KdVI Research group: Stochastics and Financial Mathematics Graduation thesis Supervisor: dr. B.J.K. Kleijn; dr. R.G. de Vilder
Do stock prices react fast to the market information?
This thesis studies how the financial information is absorbed into stock price after a corporate makes a profit warning public. We use novel estimators to measure the volatility, volume, and spread revealed in the high frequency stock prices. The observed highly volatile prices with small trading volumes upon the market opening implies market opening prices do not fully absorb the information. We also find that small cap stocks with positive profit warning have a persistent upgrade trend, such trend, however, disappears when the profit warning is negative. Moreover, large cap stocks do not exhibit such trend. The last contribution of this thesis is the introduction of the consecutive low volatility period defined as equilibrium, which serves as a general description of information absorbing process. There is moderate variation among small cap and large cap stocks: information needs more time to be absorbed into small cap stock price than large cap stock price.
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Scientific abstract (pdf 1K)   Full text (pdf 803K)

D. Wei
Master programme: Stochastics and Financial Mathematics October 30th, 2017
Institute: KdVI Research group: Stochastics and Financial Mathematics Graduation thesis Supervisor: A.V. (Arnoud) den Boer
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Decision based model selection for the newsvendor problem
In this thesis, the performance of a decision based model selection method is studied when it is applied to the newsvendor problem. The DBMS is a model selection method that selects models based on the performance of the decisions derived by the models rather than the goodness-of-fit of the underlying demand distribution. The expressions of the expected regret caused by DBMS are derived in the scenario cases where two models are available. The expressions are obtained by firstly computing the distributions of the decision and then calculating the regrets of the two decisions. The robustness measured by the maximum regret of a given decision, is discussed knowing partial information of the underlying model, and the maximum regret is shown to be achieved by a two-point distribution. The performance of DBMS is illustrated numerically when the underlying model assumes a two-point distribution. It is shown that DBMS performs better than the purely data-driven approach, based on the empirical distribution of the demands, when the performance is measured in terms of the expected cost.
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Scientific abstract (pdf 1K)   For more info or full text, mail to: A.V.denBoer@uva.nl

N. Disveld
Master programme: Mathematics MSc October 25th, 2017
Institute: UvA / Other Research group: Korteweg-de Vries Institute for Mathematics Graduation thesis Supervisor: Jasper Stokman
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Nonsymmetric Interpolation Okounkov Polynomials
There exist (non-)symmetric interpolation polynomials that are connected to the famous (non-)symmetric Macdonald polynomials. With Laurent polynomials, the role of the (non-)symmetric Macdonald polynomials is being played by the (non-)symmetric Koornwinder polynomials. There exist symmetric interpolation Laurent polynomials that are connected to the symmetric Koornwinder polynomials, we give a new proof of this existence. Also, we give a definition of the non-symmetric interpolation Laurent polynomials that are connected to the non-symmetric Koornwinder polynomials and prove their existence.
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Scientific abstract (pdf 1K)   For more info or full text, mail to: j.v.stokman@uva.nl

P. Bongers
Master programme: Mathematics MSc October 6th, 2017
Institute: KdVI Research group: Stochastics Graduation thesis Supervisor: prof. dr. R. Nunez Queija
Queuing on a continuous circle, a mathematical analysis of a void-avoiding optical fiber-loop
In this thesis, we consider a node where data packets arrive and have to be processed. A node can only process one job at the time, therefore excess jobs have to be placed in a buffer. For this purpose, an optical fiber-loop can be used. This fiber-loop creates a small time delay. When the job emerges from the fiber-loop, it can be transmitted or transferred into the fiber loop again. We begin our research by showing the relations between the fiber-model and queueing models. We describe the distribution of the queue content, the number of jobs that are in the system in steady state. In earlier literature, the mean and variance of the queue content were obtained. The goal of this master project is to understand this distribution better. We proceed by proving some properties of the model. Because direct analysis of the model is difficult, we present an approximation that makes the analysis of the model considerably easier. We show that the distribution of the number of jobs in the fiber-loop for the approximation is very similar to that of the original model, but is much easier to obtain.
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Scientific abstract (pdf 1K)   Full text (pdf 752K)

D. Mitkidou
Master programme: Stochastics and Financial Mathematics September 26th, 2017
Institute: KdVI Research group: Stochastics and Financial Mathematics Graduation thesis Supervisor: Asma Khedher
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Quadratic hedging strategies in affine models
This master thesis studies the problem of hedging European style options in incomplete markets. The most celebrated model which is often used for option pricing and hedging is the Black-Scholes model. This model imposes certain assumptions which allow to form perfect hedging strategies and therefore the risk involved in trading options is eliminated. The most signi ficant assumption is that volatility is constant over time. However, if we would like to take a more realistic view of the financial world, the latter assumption needs to be relaxed. In the context of this thesis, we consider stochastic volatility models, where the volatility is modelled as a stochastic process. In this class of models perfect hedging strategies do not exist. Our goal is to form such strategies that reduce the risk as much as possible. To approach this problem we use a method called quadratic hedging. Affine stochastic volatility models constitute one subclass of stochastic volatility models. They are of special interest due to their computational tractability which often allows to obtain closed-form solutions for pricing several options. This thesis uses the rich structural properties of affine models to obtain semiexplicit formulas for quadratic hedging strategies.
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Scientific abstract (pdf 1K)   Full text (pdf 568K)

P.A. van Reeuwijk
Master programme: Mathematics MSc September 15th, 2017
Institute: KdVI Research group: Algebraic Geometry Graduation thesis Supervisor: Arno Kret
The Langlands-Kottwitz method for the modular curve
A moduli space is a space parametrising geometric objects; these are objects of primary interest in algebraic geometry. These spaces, however, are often very complicated. From a moduli space a zeta function can be construced, a complex function that, being an anayltic object, is supposed to be much easier to handle while still containing valuable information on the geometry and arithmetic of the moduli space. For this to work, the zeta function needs to satisfy a number of anaylic properties. We use the approach of Langlands and Kottwitz to work towards understanding the zeta fuction of moduli spaces of elliptic curves: we can use the special properties of these elliptic curves to explicitly count the number of points on their moduli spaces, leading to a better understanding of the properties of the zeta function.
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Scientific abstract (pdf 1K)   Full text (pdf 220K)

I.C. Bodin
Master programme: Stochastics and Financial Mathematics August 31st, 2017
Institute: UvA / Other Research group: Korteweg-de Vries Institute for Mathematics Graduation thesis Supervisor: Peter Spreij
Pricing and Hedging of Mortgage Option
This thesis provides different pricing methods for four mortgage options, namely the pipelineoption, the meeneemoption,the LtV-option and rentemiddeling. A theoretical approach is present for each option and also the results of numerical experiments are presented. Common techniques are Monte Carlo, trinomial trees and Lévy theory. Real data is used to calibrate the models to guarantee the most relevant results. These turn out to be in line with the result of the currently used behaviour models in case of European options. American options are differently priced and the bank should be aware of the possible consequences.
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Scientific abstract (pdf 1K)   Full text (pdf 6498K)

M.J.M. Derksen
Master programme: Stochastics and Financial Mathematics August 29th, 2017
Institute: KdVI Research group: Stochastics and Financial Mathematics Graduation thesis Supervisor: Peter Spreij
Pricing of Contingent Convertible Bonds
In this thesis different pricing models are studied for the pricing of Contingent Convertible bonds (CoCos). These are special type of bonds, which convert into equity or are written down, when the capital of the issuing bank becomes too low. In this way, outstanding debt is reduced and capital is raised, to strengthen the capital position of the bank. In practice, this conversion is typically triggered by the capital ratio of the issuing bank falling below some threshold or by a regulator calling for conversion. However, in all of the existing pricing models the conversion of CoCos is triggered by a market value, like a stock price, falling below some threshold. In this thesis a model is proposed, in which the market cannot observe the true asset value process, but it only has access to noisy accounting reports, which are only published at discrete moments in time. In this way, the price of CoCos can only be based on the information from the accounting reports, not on the true asset process.
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Scientific abstract (pdf 1K)   Full text (pdf 811K)

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