Numerical Methods for Stochastic Differential Equations

Introduction to Ito and Stratonovich calculus for stochastic integrals, 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).

First there will be a set of exercises and then the students will work (alone or in teams of two students) on a project and finally there will be a written exam.

The assessment criteria are:

• the theoretical depth of the knowledge about stochastic differential equations

• the ability to apply the knowledge to a practical problem

• the ability to implement numerical methods correctly

The grade is based on the exercises (10%), the report about the project (45%) and the written exam (45%).

In case of insufficient results for the exercises assignments, the report or the oral exam, a repair option may exist in accordance with Article 2, Examination requirements, Clause 4, of the Implementation Regulations 2023-2024.