Stochastics and Financial Mathematics
The programme in a nutshell
The Master’s programme in Stochastics and Financial Mathematics is a two-year programme, divided into four semesters. The last semester you will dedicate to the master project, which is either a research project or an external project.
Courses
During the first semester, you will take the only compulsory course: Measure Theoretic Probability. This forms the foundation for the more advanced subjects to come. Each year the department provides a list of recommended courses from which you will select four or five subjects each semester. Some examples of subjects offered are:
- Mathematical Statistics
- Stochastic Integration
- Percolation Theory
- Interest Rate Models
- Stochastic Processes
- Stochastics Optimization Ergodic Theory
In consultation with the staff, it may be possible to substitute some of the recommended courses with certain other relevant mathematical modules, such as Partial Differential Equations or Functional Analysis.
Course descriptions
Further information about the Master’s programme in Stochastics and Financial Mathematics including the list of recommended courses for the current year can be found here.
Master project
The Master’s programme concludes with a research project or with an external project carried out at a business or research facility outside the Department of Mathematics. This final project will fill the last semester. Your mentor can help you to find a suitable project. The project culminates in writing your Master’s thesis and giving an oral presentation of the results.
Examples of topics for master projects are:
Risk management in banks
Analysing the risks associated with financial assets is at least as important as analysing their yields. Incidents like the sub-prime mortgage crisis have made this painfully clear. How can statistical and probabilistic methods contribute to the risk management procedures of financial institutions?
Valuation and hedging of derivatives
Master theses may study the pricing of exotic options in equity or fixed income, as well as hybrid constructions in a model or a model-free context. Alternatively they may concern stochastic volatility models or arbitrage-free models for the term structure of interest rates. Developing the underlying mathematical tools and concepts needed in finance (involving areas like stochastic analysis, Levy processes, complex analysis or PDEs) can also be the topic of a master project.
How fast can a Bayesian procedure learn an unknown function?
In many settings data is used to determine an unknown response curve, probability density or regression surface. One method is to model such a function a-priori as a sample path of a Gaussian or other process and reconstruct it by Bayes' rule. Does this work? Can one express the precision of the procedure in terms of the amount of information in the data?
Using mathematics to find genes
Finding the genes responsible for complex diseases is like looking for a needle in a haystack. Thorough statistical and computational methods are essential for separating signal from noise in experimental and population data. This is an example of true synergy between mathematics and the life sciences.
More information about research of the department can be found here.
Internships
You are offered the opportunity to carry out your master project externally at a business. VU University Amsterdam maintains close contact with many financial businesses, yielding internship possibilities in plenty. For more information on internships and work placement opportunities, you can consult the website of the Internship Office for Mathematics and Computer Science.
