Entry requirements

120 credits including 90 credits in Mathematics

Learning outcomes

The course aims to provide basic knowledge of parabolic partial differential equations and their relationship with stochastic differential equations and related applications.

In order to pass the course (grade 3) the student should be able to

• give an account of the Ito-integral and use stochastic differential calculus;
• use Feynman - Kac's representation formula and the Kolmogorov equations;
• give an account of the theory for stochastic control, optimal stopping problems and free boundary problems;
• apply the theory to financial problems;

Content

Stochastic calculus and diffusion processes. The Kolmogorov equations. Stochastic control theory, optimal stopping problems and free boundary problems. Integro-differential equations.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.