Mathematics for Oceanographic Measurements project available for master's thesis project

Jason Frank (Mathematical Institute, MI) and Leo Maas (Institute for Marine and Atmosphere research Utrecht, IMAU) are looking for a student to research the design of an instrument for measuring water flow in the ocean or laboratory. The device will measure motions normal to the faces of the icosahedron. Measurements are triangulated to infer the full three-dimensional velocity field. Redundancy due to symmetries may be used to quantify uncertainty and detect noise. Rigid body motion of the instrument needs to be detected as well. Interesting about this project is that if the results appears to be promising, a prototype will actually be built! The project combines aspects of geometry, approximation theory and data science/statistics. 
For more information, please contact Jason Frank.

Research projects available in the area of Applied Mathematics to Climate Science 

If you are interested in a research project oriented to mathematical problems such as climate change, climate prediction, atmosphere and ocean predictability, using physics-informed or data science tools (data assimilation, machine learning, dynamical systems), please contact Alberto Carrassi. The research projects will entail a period abroad at the Departement of Meteorology of the University of Reading (UK).

Other available internship projects

Note that both Rabobank and Sioux LIME offer several internship projects. The internships can be combined with your thesis project.

Examples of internships

Here you find examples of internships that students took in recent years for their thesis project. Contact details of the companies and research institutes where the internships were conducted can also be found. If available, a link to the thesis is provided.

Contact persons. Markus Hofer and Geert-Jan Bralten

Thesis. An analysis on corporate credit-adjusted hedging strategies

Abstract. Hedging strategies of a corporation are aimed at managing financial risk. Our analysis focuses on the risk induced by moving interest rates and foreign exchange rates. The interest rate swap and the cross-currency swap are popular derivatives to mitigate these risks. Matching the tenor of such a swap to the duration of the risk-exposure yields a perfect hedge, but this can be costly for longer time spans. A rolling strategy constructed from several consecutive swaps with shorter tenor can be a cost-saving alternative, but this implies a roll-over risk. Our objective is to quantify the trade-off between the potential gains and risks associated to rolling hedging strategies.

Contact person. Bert de Bock

Thesis 1. Dynamic Replicating Portfolio Models

Abstract. Savings accounts represent a large part of the funding of a bank. The bank wants to use this money for investments, but this is associated with a risk. The clients can freely deposit or withdraw money at any time they choose to and therefore, a savings account does not have a predetermined maturity. Assumptions regarding the maturity must be made and a savings account is therefore modeled by a portfolio that consists of fixed-income securities that mimics the cash flows of the account. There are multiple ways to create such a replicating portfolio model. During my internship, I created a dynamic model which forecasts the unknown risk factors, such as the market rates, the client rate and the volume, and provides the user with a dynamic investment rule, which states how to invest the available money for every time step. The model has also been tested on actual data and the results are compared with the results of a static model. In a static model the investment rule is constant in time. This means that maturing money is always reinvested in the same maturity and available money is always allocated according to the same percentages.


Thesis 2. One-Way Trading With Transaction Costs

Abstract. In the one-way trading problem a trader initially has all his capital invested in shares. He wishes to sell all his shares on the stock market to maximize his final cash. Vovk showed that there are certain trading strategies that will guarantee some final amount of cash, depending on the maximum observed price. He also characterized the best possible guarantees and their corresponding strategies. In reality a trader has to pay a fee to a broker for every transaction. When transaction costs are added to the one-way trading model, Vovks strategies can result in very large losses. We adjusted the strategies such that they trade more economically. We showed they perform almost as good as Vovks strategies for the transaction cost free model.


Thesis 3. On the optimal investment policy for a dormant pension fund with fixed liabilities

Abstract. In recent years, due to the aftermath of the credit crisis and the euro crisis, interest rates have hit record lows. Low interest rates increase the costs or discounted value of pension plans and pension funds. Historically and in recent years stocks, on average, had higher yields than bonds. The question that arises is if it is possible to have a pension plan, which utilises risky assets such as stocks, with lower costs and still is considered to be safe enough.


Thesis 4. Calculating a Dutch Pension Fund’s Capital Requirement for Longevity Risk

Abstract. Longevity risk is the risk arising from uncertainty in the prediction of future mortality. This risk must be faced by pension funds. The legislation for Dutch pension funds prescribes that the pension funds need to keep in reserve a certain level of capital for this risk. De Nederlandsche Bank (DNB) suggests a method for calculating this capital requirement. Problems with this method are that it is generalized, not transparent and it does not make use of recent insights in mortality. Therefore, in this thesis an alternative method is developed, that provides a better insight in the current risk. This alternative method is a Monte Carlo method, using a stochastic mortality model. The stochastic model used is recently published and is calibrated on the most recent data. Finally, the capital requirement is calculated using both methods. It turns out that the resulting capital requirement from the alternative method is less than half of the capital requirement calculated using the method suggested by DNB.


Thesis 5. Macro-Level and Micro-Level Claims Reserving for Non-Life Insurances

Abstract. Insurance companies need to hold capital aside to meet future liabilities associated with events that are covered by existing contracts. The process of estimating the reserves is called claims reserving. Macro-level reserving models are already used for decades by insurance companies. This is because they are widely applicable and easy to use. With the introduction of Solvency II, a regulatory framework for insurances, insurance undertakings are encouraged to explore more advanced reserving models. The main goal of this thesis is to investigate whether the claims reserving process for non-life insurances can be improved. In the macro-level models, a lot of useful information that is often available remains unused. This leads to introducing a micro-level reserving model, which can take into account much more detailed information than the macro-level models. For this thesis, a macro-level model and a basic micro-level model are implemented. Where the macro-level model only gives projections of the aggregated payment amounts, the micro-level model allows for examining the projections for every single claim. Because of this, every component of the micro-level model can be tested and adjusted individually (reporting delay, claim development, payment distributions). Based on the results of the out-of-sample tests, it can not be concluded that one model performs better than the other. For this, the models should also be tested on other data sets. With further research, adjustments can be made such that the micro-level model is suitable for application in practice. Based on the findings in this thesis, insurance companies could improve the possibilities for applications of micro-level reserving models by preparing their data and the registration of it. Therefore, more awareness should be created at insurance and reinsurance companies about the micro-level model and the required data quality.


Thesis 6. An investment strategy for pension funds, with the focus on the purchasing power of the pension entitlements

Abstract. Currently, more than 50% of the participants of a pension fund have a pension funds that has a funding deficit. Those pension funds are not allowed by law to index the pension benefits of their participants to the inflation. This results in a decrease in purchasing power of the pension entitlements. In this talk we first look at the historical performance of stocks and bonds. Based on these results we will introduce an investment strategy for pension funds that should better preserve the purchasing power of its participants. This strategy will be applied on a model pension fund and compared with a common investment strategy of pension funds.

Contact persons. Pieter-Jan van Kessel and Marvin Oeben

Thesis 1. Binary Classification on a Highly Imbalanced Dataset

Abstract. Credit card fraud is a growing field of crime. Data-drive detection of fraudulent transactions can be viewed as a binary classification problem, where the two outcome classes are highly imbalanced. To overcome the difficulties that arise from this imbalance, multiple solutions are described and explored. Furthermore, accompanied statistical arguments, a novel method using subgroup discovery is introduced. Finally, all methods are empirically tested on an actual credit card transaction dataset.


Thesis 2. Generalized Linear Mixed Models in the competitive non-life insurance market

Abstract. For the last decades, Insurance companies have used Generalized Linear Models to predict the risk of harm on non-life insurance policies. These risks drive the price of the policy provided to the market. Recently, the market has changed into a highly competitive market due to the ease of entering a contract through the internet. This thesis studies the behavior of the highly competitive non-life insurance market and the possible problems that can occur when using the Generalized Linear Model for premium pricing and whether an extension of this model, the Generalized Linear Mixed Model can provide better premiums for this market.


Thesis 3. Dynamic Layered Pooling; a method of mitigating risk by sharing future losses

Abstract. PwC has developed the Dynamische Huur Stabilisator (DHS) which stabilizes the cash flow of a real estate fund by sharing the future vacancy risks with other real estate funds. This translates to a higher valuation of their properties and better conditions on debt capital. The underlying innovation of this construction is the use of dynamic and layered pooling of the lease contracts in the participating real estate funds. We provide the mathematical framework of the DHS and give a quantitative analysis of the risk reduction under different conditions. We examine both analytical and numerical solutions, by using Monte Carlo techniques.

Contact person. Jelle van Luipen

Thesis. On the reduction of train delays caused by external factors

Abstract. Spoorlopers (or railway walkers, meaning people who walk along the railway unauthorized) cause almost 4 hours of train delays per day, meaning they make up almost 20% of all train delays. ProRail has been looking for ways to reduce the number of railway walkers. One way of reducing the number of railway walkers is predicting the time and location where these people appear, thus allowing ProRail to take preventive measures. In this thesis, we present two machine learning methods, support vector machines and neural networks, which we use to build models that can predict the time and location where people will appear on the railway, based on historical data. A large part of this thesis is dedicated to explaining both these methods. In order to improve our models and reduce computation time, we use two dimensionality reduction techniques, principal component analysis (PCA) and ReliefF. We will create our models in Matlab, and compare them to a benchmark model, provided by ProRail.

Contact person. Hans van Leeuwen

Thesis. Capital Valuation Adjustment for Bermudan Options by the Stochastic Grid Bundling Method

Abstract. Since the introduction of the Basel III regulations Banks have started to recog- nise the impact of the rising capital requirements on their derivatives in the form of capital valuation adjustment (KVA). One of the main drivers of this valuation adjustment are the costs related to the holding of counterparty credit risk capital. The numerical aspects of the computation of these costs in a standard Monte Carlo approach would result in heavily nested simulations, which is computationally unattractive. Jain, Karlsson and Khandai have proposed a way to circumvent this nested simulation situation by means of using the Stochastic Grid Bundling Method, as introduced by Jain and Oosterlee. This thesis presents a new way of applying this approach to price the KVA related to counterparty credit risk for Bermudan options.

Contact person. Diederik Fokkema

Thesis 1. Robust estimation in operational risk modeling

Abstract. Over the last two decades, the modeling of operational risk has become increasingly important and it is nowadays mandatory for banks to allocate a capital charge to cover most large-scale operational losses. When standard estimation techniques are used, such as maximum likelihood, the estimated capital charge is highly sensitive to minor contamination of the operational loss data. This is a major issue an practice: large swings may be produced in the capital charge when a single or a few loss events are added to the database. In order to ensure stable capital charges, we introduce the robust statistics framework, which is aimed at sacrificing some efficiency at the exact model, in order to gain robustness against minor deviations of the model. We show that using robust estimation techniques, the estimated capital charge maintains high efficiency at the exact model, while remaining stable under contamination of the operational loss data.

Thesis 2. Credit risk modeling using a weighted support vector machine

Abstract. The modeling of credit risk is traditionally based on approaches such as linear regression or multiple discriminant analysis. There are several limitations to these methods, in particular their inability to adapt to new data and the assumption of a certain (linear) relation between the dependent and independent variables. In this thesis we will use a new machine learning technique called weighted support vector machine combined with averaged stochastic gradient descent. Using this approach, we create a classification of a data set containing mortgage loans of Freddie Mac into several groups with increasing probabilities of default. This method shows promising results, both in terms of predictive and discriminatory power, especially when information about the monthly performance of these loans and the macro-economic situation is included. If the performance on other data sets is similar, the technique can be implemented for credit risk modeling.

Thesis 3. A Regime Switching Jump-Diffusion Model and its Application to Credit Risk and Option Pricing

Abstract. A vital issue in financial mathematics is the choice of an appropriate model for the fi nancial market. It is well-known that the famous Black-Scholes model does not perform well in reality. In this talk we will extend the Black-Scholes model in order to improve its empirical performance. The extended model, the so-called ``regime switching jump-diffusion” (RSJD) model will be applied to credit risk and option pricing. Moreover, we will discuss some calibration techniques and we will see that calibration is feasible for this model. As a test example, the RSJD model will be applied to a real firm that has been in financial distress recently.

Contact person. Victor Popa

Thesis. Analysis of savings rate and deposit volume models for replicating portfolios of non-maturing accounts 

Abstract. The focus of this research is to improve on existing savings rate and deposit volume models used for constructing replicating portfolios of non-maturing accounts (NMAs). Such accounts have proven difficult to model, especially, as they offer savings rates to clients that change infrequently and with discrete jumps. The thesis uses savings rate and deposit volume data from both the Netherlands and Germany for a period of eight years. The data was kindly provided by NIBC Bank N.V., a Dutch corporate bank. Savings rates are modeled with a latent process that governs when changes occur. The model of the deposit volumes is chosen with an iterative Box-Jenkins procedure from an ARIMA family of models. The research project is fully implemented in MATLAB and can be directly used with common approaches to constructing and valuating replicating portfolios of non-maturing accounts.

Contact person. Rob Naber

Thesis. Modelling Electricity Spot and Future Prices

Abstract. Since 2007, the electricity markets throughout Europe have undergone massive changes due to deregulation. As a result more and more electricity is traded on electricity markets for day-ahead delivery or in the form of futures contract. The spot electricity prices are extremely volatile therefore being able to predict its movements could result in more certainty for a buyer or seller of electricity. The fact that it is hard to store electricity makes this market different from other commodity markets. The dynamics of the electricity spot prices show seasonal and volatile behaviour with suddenly occurring extreme spikes. Therefore conventional time series models will not be able to mimic this market. A Lévy driven CARMA model, the continuous analogue of the ARMA process, is proposed as its dynamics could be a good fit for the specific behaviour of the spot electricity prices. Furthermore the CARMA model will give rise to a pricing measure of electricity futures. In this thesis the properties and estimation of the Lévy driven CARMA process will be discussed and applied to the, Dutch electricity market, APX. It will be shown that a CARMA(3,2) model is the best fit.

Contact person. Hannes Muehleisen

Thesis. Estimating Aggregates over Joins

Abstract. Approximate Query Processing is the field that speeds up queries on databases by using approximations. Specifically, we will study estimation of the sum over a join between two relations. Instead of taking a sum directly, we estimate the total sum from a sample. We introduce a novel algorithm to take a weighted sample of the join result without calculating the join explicitly. For even more speedup, we introduce the first heuristic weighted sampling algorithm.

Contact person. Hendrik Dijkstra

Thesis. A New Method to Determine Maximum Perturbation Growth in a Quasi-Geostrophic Ocean Model

Abstract. Analysing growth of initial perturbations in dynamical systems is an important aspect of predictability theory because it tells us which factors have the strongest influence on the system. For linear systems, these factors are the modes with the largest eigenvalues. For non-linear systems, we consider the conditional non-linear perturbation (CNOP). These can be found by solving a non-linear constrained maximization problem, which is typically done using sequential quadratic programming (SQP), a routine that requires an adjoint model. Such adjoint models are are not always available. Therefore, we study two adjoint-free methods: PSO and COBYLA. Because such methods typically work best on low-dimensional problems, we apply dimension reduction. We use the proposed methodology to find the CNOPs of a quasi-geostrophic ocean model. We find that COBYLA outperforms PSO and is able to find reasonable CNOPs, although at a higher computational cost than conventional adjoint-based methods.

Contact person. Lex Dielen

Thesis. Minimizing the waiting time in a large-scale network of an advanced planning system

Abstract. My thesis is written during an internship at the software company ORTEC. It analyses a heuristic for minimizing the amount of waiting time in a real-life schedule of an advanced planning system. The problem considered is part of the larger problem to allocate resources to a set of orders, where the capacity of the vehicles varies, and time windows can be specified for pickups and deliveries. Furthermore, regulations on the drivers working hours are taken into account. The algorithm used by ORTEC to minimize the amount of waiting time in the schedule is constrained in such a way that no structural changes are allowed. This means that, amongst others, orders cannot be assigned to different resources and the sequence of pickups and deliveries is not allowed to be changed during the minimization process. Only the start and finish instants of the actions in the schedule are allowed to be changed. The method used to reduce the waiting time in the trip is binary search. The conditions leading to a bifurcation of the search domain are identified. A framework is implemented to prevent this bifurcation, since the algorithm does not handle it correctly.

Contact persons. Fieke Dekkers and Jacco Wallinga

Thesis 1. Bayesian Inference of Phylogeny Using Variable Number of Tandem Repeats and Markov Chain Monte Carlo

Abstract. We implement and evaluate methods to infer the phylogeny of Variable Number of Tandem Repeats (VNTR) isolates of tuberculosis through Bayesian inference and Markov Chain Monte Carlo, using an existing transition rate matrix (Sainudiin, 2004). By also inferring the phylogeny through the model of Hasegawa, Kishino and Yano (HKY) using nucleotide data of the same isolates, we are able quantitatively and qualitatively compare the phylogenies obtained through both models. By simulating data, we assess how well the true phylogeny can be inferred for both the Sainudiin and HKY model, for different levels of mutational saturation in the data. We show how both the Sainudiin and HKY model can be combined to yield a phylogeny that is better resolved and more accurate than by the use of either model. By changing the model for the mutation rate proportionality in the Sainudiin model, we are able to use the estimates of the model parameters to speculate on the mechanisms by which VNTR mutates. The developed methods have been made available in the package BEASTvntr for BEAST2.


Thesis 2. The relative impact of import compared to transmission within the Netherlands on new latent tuberculosis infections

Abstract. Although the Netherlands is a low-incidence country, elimination of tuberculosis (TB) is not realistic with the current control and prevention strategies. Since most TB cases are foreign-born, knowing which route of transmission contributes most to immigrant TB cases could help change the current control strategy in order to reach TB elimination. Few is known on the transmission dynamics within and between immigrant groups and therefore we aim to determine the relative impact of import (by immigration and traveling to country of origin) compared to transmission within the Netherlands on new latent tuberculosis infections (LTBIs). We use data from 1995 until 2012 from the National Tuberculosis Registry (NTR) and Statistics Netherlands (CBS) to develop compartmental SEIR models for autochthons, Moroccan, Turkish and Somali first generation immigrants (FGIs). Using the maximum likelihood method we estimated the transmission rates for every ethnic group. With those estimates we calculated the relative impact of import compared to transmission in the Netherlands on new LTBIs. The results suggest that entrance screening for LTBI could be effective for Moroccan and Turkish FGIs. For Somali FGIs, however, the reduction of tuberculosis infection would be limited and control strategies should focus on reducing transmission in the Netherlands.


Thesis 3. Mathematical modeling of the transmission dynamics of hepatitis B using phylogenetics

Abstract. In the Netherlands, the hepatitis B virus spreads mostly by unsafe sexual contacts, especially among men who have sex with men. Most infected individuals recover three to four months after acquisition of the virus and obtain life-long immunity. However, in some individuals the acute infection progresses to a chronic infection. Although chronically infected individuals are longer infectious, it is unknown how important the chronic state is in the spread of the disease. For the effectiveness of the current vaccination program this is an important question. It is difficult to answer this question by standard epidemiologic methods because the hepatitis B infection is often asymptomatic and most transmission events are unobserved. We use the DNA sequences of the virus collected from both acutely and chronically infected individuals to construct a family tree of the viruses, a so-called phylogenetic tree. From this phylogenetic tree we estimate the transmission dynamics of the disease by using two different models; a birth-death branching model and a coalescent model.

For more information about internships, please contact the internship coordinator Dr. P.A. Zegeling.

GSNS Internship Infographic

Research projects

Within all Master's programmes one or more research projects are mandatory (see ‘Study programme’ for general information).

  • within the university, step 1 only
  • outside of the university, in the form of an internship at a company or research institute. 
    • in The Netherlands, step 1 and step 2
    • abroad (see also: ‘stay abroad’), step 1, step 2 and step 3

It may also be possible to do an extracurricular internship; less research-oriented but more geared towards applying skills learned in your Master's programme and getting a closer experience of a real company environment. Please ask your programme coordinator for opportunities within your programme.

Specific for Nanomaterials Science students: an additional (international) internship as secondary elective besides your research project is possible. Please look at the Internship Nano page for extra information.

Specific for Applied Data Science students: it is not possible to go abroad for internship. All internships have to be done in the Netherlands.

Specific for Artificial Intelligence, Applied Data Science, Business Informatics, Game and Media Technology, Computing Science, Human Computer Interaction, Mathematical Sciences, and Nanomaterials Science:

You are required to apply for approval of your research project by submitting a request via OSIRIS Case. Important: in order to apply completely and correctly, you must have discussed the project setup with your intended project supervisor beforehand! 

  • Please select ‘My Cases’, ‘Start Case’ and then ‘Research Project GSNS’ or 'Thesis Project ADS'.
  • We advise you to study the request form previous to discussing it with your supervisor, or fill it out together, to make sure you obtain all of the information required.
  • After submitting your request, it will be forwarded to your master’s programme coordinator, the board of examiners and student affairs for checks and approvals.
  • After approval of your project it will be automatically registered in Osiris. If something needs to be amended, you will be notified by email.

Specific for Climate Physics, Theoretical Physics, Experimental Physics and History and Philosophy of Science:

  • Fill  out the research project application form and get signatures.
  • Your supervisor wants to change the copyright clause in the research application form -> contact the research project coordinator.
  • If your research project is outside of the UU a work placement agreement is obligatory (see step 2). If you are going abroad you also need to do a Stay Abroad request in Osiris (see step 3)
  • Otherwise e-mail the application from to the Student’s Desk GSNS,, to start the approval process by the Board of Examiners.

Specific for Artificial Intelligence, Applied Data Science, Business Informatics, Game and Media Technology, Computing Science, Human Computer Interaction, Mathematical Sciences, and Nanomaterials Science:

  • Your research project is outside the UU-> use the GSNS work placement agreement and get the signature of the host organisation.
  • If the host organisation requires changes in the GSNS work placement agreement -> contact the internship contract coordinator
  • If the host organisation only uses its own agreement -> contact the internship contract coordinator
  • In all cases the signature of the internship contract coordinator is needed. If the UU is no party in the host organisation agreement the approval of the internship contract coordinator remains necessary. In some cases an appendix to this kind of agreement has to be drafted and signed by all parties.
  • Upload the fully signed work placement agreement with your application form to Osiris Case to start the approval process by the Board of Examiners. Be aware, for a research project outside Utrecht University a signed placement agreement is necessary to get approval.

​Specific for Climate Physics, Theoretical Physics, Experimental Physics and History and Philosophy of Science:

  • Your research project is outside the UU-> use the GSNS work placement agreement and get the signature of the host organisation.
  • If the host organisation requires changes in the GSNS work placement agreement -> contact the internship contract coordinator
  • If the host organisation only uses its own agreement -> contact the internship contract coordinator
  • In all cases the signature of the internship contract coordinator is needed. If the UU is no party in the host organisation agreement the approval of the internship contract coordinator remains necessary. In some cases an appendix to this kind of agreement has to be drafted and signed by all parties.
  • Email the fully signed work placement agreement to the Student's Desk GSNS:
  • If your research project/thesis is outside of the Netherlands you have to do a Stay Abroad request in Osiris Student after receiving the approval by the Board of Examiners. Information can be found on the webpage Stay Abroad. Please read the whole page carefully. If you have questions please contact the international office. Be aware that arranging a research project abroad takes time.
  • You might find this checklist useful during the organisation of your traineeship abroad.
  • It is important to check the travel advice for your destination given by the Ministry of Foreign Affairs. Please type in your destination on the website (in Dutch). If your country has orange or red areas your Stay Abroad request cannot be validated.

Job board

Career Services collects vacancies that are relevant to science students in this job board. Are you looking for a student job, internship or starter job? Create  a profile and discover exclusive job opportunities!

You can also check the Career Services Internship Listings to see if any of the internships interests you. Companies and organisations looking for interns from the university's various academic programmes often post their vacancies there.