Mathematics in Progress

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Displaying theses 1-10 of 432 total
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W. Swijgman
Master programme: Mathematics November 9th, 2018
Institute: KdVI Research group: Dynamical Systems and Numerical Analysis Graduation thesis Supervisor: Ale Jan Homburg
Growth dynamics of cross-feeding microbes
Cross-feeding means that an essential (scarce) nutrient for a microbe is produced by another microbe. Several systems of microbial cross-feeding communities are studied in which for every microbial species (at least) one nutrient is scarce in the environment and only produced by another species in the system. In certain settings it is possible that this cross-feeding can keep on going so that the microbial concentrations grow infinitely large as time approaches infinity. Since we want to study what happens to the growth rates and the relative concentrations in this case, a transformation of the space to a compact set (the Poincare sphere) is done. That is, the original (planar) dynamics are projected onto a sphere such that infinity is mapped onto the equator; we can now study what happens on the sphere and in particular what the dynamics near/on the equator are.
picture that illustrates the research done
Scientific abstract (pdf 1K)   Full text (pdf 7970K)

G. Puccetti
Master programme: Mathematics November 8th, 2018
Institute: KdVI Research group: Stochastics Graduation thesis Supervisor: Michel Mandjes
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Average nearest neighbor degree in geometric inhomogeneous random graph
Random graphs are a mathematical way to describe real networks, such as social networks or the world wide web. In the model we study, vertices are provided with weights and positions in a circle. The probability for two nodes to be connected is dependent on both these quantities. We describe the effect that the presence of distance has in this model, particularly on the average nearest neighbor degree, a quantity that makes us understand the degree of the neighbors of certain vertices. After this is done we implement an algorithm to simulate instances of this model and to study it numerically, looking at its clustering coefficient.
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Scientific abstract (pdf 1K)   For more info or full text, mail to: m.r.h.mandjes@uva.nl

H. Zhang
Master programme: Stochastics and Financial Mathematics October 30th, 2018
Institute: KdVI Research group: Stochastics and Financial Mathematics Graduation thesis Supervisor: prof.dr. R. Nunez Queija
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Capacity and Efficiency Analysis of Multiserver-Queuing Systems
Imagine you are a member of a strategy committee and are supposed to decide to put some servers in the system. You can either put a fast single server or c servers that the sever speed is c times slower than the single one. What will you choose? This research focuses on some specific queuing systems and both theoretically and numerically comparison based on first-come-first-serve service discipline and one-by-one arrival assumption. For $M/M/cdot$ systems, single fast server is the best, but for more variable distributions that will not be true. Analytical solutions of multiserver systems are hard to obtain. For that matrix-geometric approach allows to study multiserver systems with so-called phase-type distributions, that can be used to approximate any general distribution as closely as desired. For future studies it may be relevant to reconsider some of the assumptions made in this thesis. For example, some features of systems like the service discipline (first come first serve, random order, last come first serve), the behavior of customers, the arrival process (one by one or in batches) and service capacity, all lead to different level of efficiency to systems.
picture that illustrates the research done
Scientific abstract (pdf 1K)   Full text (pdf 2566K)

T.M.R. Hesselink
Master programme: Mathematics October 29th, 2018
Institute: KdVI Research group: Stochastics Graduation thesis Supervisor: J.H. van Zanten
Optimal Bayesian distributed methods for nonparametric regression
In this thesis we will consider Gaussian processes making use of both the Matérn kernel and the squared exponential kernel. However neither of these Gaussian process priors lead to scalable Bayesian methods and therefore they are highly impractical for large data sets. To solve this, we turn to the distributed setting where we divide the data of size $n$ over $m$ machines, which collectively help to compute a global posterior. For the distributed setting, we will consider multiple methods, which consist of changing the local posterior and different aggregation methods for the local posteriors. These methods will be studied via simulation. We will pose theoretical results for some of the methods. Finally, we will perform simulation studies using the squared exponential kernel, which will show to perform similarly to the Matérn kernel.
picture that illustrates the research done
Scientific abstract (pdf 1K)   Full text (pdf 1419K)

B. van Brussel
Master programme: Stochastics and Financial Mathematics October 23rd, 2018
Institute: KdVI Research group: Stochastics and Financial Mathematics Graduation thesis Supervisor: Jan-Pieter Dorsman
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Simulating the patient flow on the Short Stay Unit
For this thesis I did an internship at the Amsterdam UMC. The subject of this thesis is the bed occupation of the Short Stay Unit at the VUmc. I have built a simulation model for the arrivals and departures. With this model I was able to predict the effects of certain policy changes. Examples of these changes were the increased inflow of patients from other wards and the effects of changing the opening times.
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Scientific abstract (pdf 1K)   Full text (pdf 3337K)

L. Raounas
Master programme: Stochastics and Financial Mathematics October 17th, 2018
Institute: UvA / Other Research group: Korteweg-de Vries Institute for Mathematics Graduation thesis Supervisor: Asma Khedher
Conic Swaption Pricing With Displaced SABR
If the market is liquid and complete, then the classical financial framework offers an unambiguous pricing method for all financial products, through the use of the risk-neutral measure. We thus have the rule of the "one price". However, in illiquid markets, the price of a product depends on the market direction, i.e. whether it is being bought or sold. This leads to the difference between the buying and the selling price, called the "bid-ask spread", to become non-negligible. Conic Finance offers a framework in which easy to compute formulas are derived for the direct calculation of both the bid and the ask prices. The SABR ("Stochastic Alpha Beta Rho") model is a stochastic volatility model used to calculate forward values of a derivative's underlying, for example the price of a stock or an interest rate. In the current post-crisis environment, interest rates are very low and sometimes even negative. To deal with this situation, the Displaced SABR extension of SABR was developed. In this thesis, we follow the Conic Finance approach and use the Displaced SABR model in order to directly price the bid and ask prices of swaptions, i.e. derivatives in which the underlying is a swap.
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Scientific abstract (pdf 1K)   Full text (pdf 1808K)

T.E. ter Bogt
Master programme: Stochastics and Financial Mathematics October 17th, 2018
Institute: KdVI Research group: Stochastics and Financial Mathematics Graduation thesis Supervisor: dr. Asma Khedher, prof. dr. Michel Vellekoop
Arbitrage-Free Interpolation in the LIBOR Market Model
The LIBOR Market Model is a mathematical model for interest rates, which provides information on a limited number of (forward) interest rates, applying to some specific time periods. Sometimes, an interest rate applying to a different time period is required. This thesis develops a new interpolation method for interest rates in the LIBOR Market Model. Unlike some other methods, it can be used when interest rates are negative. The new interpolation method ensures that interpolated interest rates have a volatility which is close to the volatility of the interest rates provided by the LIBOR Market Model, which is important in applications. The effects of the new interpolation method on the calculation of CVA for interest rate derivatives using the LIBOR Market Model are also considered.
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Scientific abstract (pdf 1K)   Full text (pdf 2089K)

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
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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.
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Scientific abstract (pdf 104K)   Full text (pdf 1581K)

M.F. Perez Ortiz
Master programme: Mathematics September 20th, 2018
Institute: KdVI Research group: Stochastics Graduation thesis Supervisor: Harry van Zanten
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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.
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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
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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.
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Scientific abstract (pdf 1K)   Full text (pdf 590K)

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