TW3750TU

Numerical Methods for Stochastic Differential Equations

Lecturer: Prof.dr.ir. A.W. Heemink, Instructor: Prof.dr.ir. H.X. Lin

Contents

Introduction to Ito and Stratonovitz calculus for stochastic integrals, Stratonovitz calculus, modelling uncertainty using stochastic differential equations, Numerical schemes for stochastic differential equations, strong order of convergence, weak order of convergence. Applications in financial mathematics (option pricing) and environmental modelling (pollution transport).

Study Goals

The student will learn to model uncertainty using stochastic differential equations.
He/she will gain knowledge about stochastic calculus, the theory of stochastic differential equations and the theory of numerical approximation of stochastic differential equations. 
He/she will get practical experience with a number of numerical methods and with implementing numerical methods using a scientific programming language.

Education Method

First there are a series of lectures about the theory including a number of exercises that have to be worked out. The second part is a project where the students have to implement a number of numerical schemes for a practical simulation problem and have to evaluate the performance of the various numerical methods.