Partial Differential Equations with Applications to Finance

5 credits

Syllabus, Master's level, 1MA255

A revised version of the syllabus is available.

Code: 1MA255
Education cycle: Second cycle
Main field(s) of study and in-depth level: Financial Mathematics A1N, Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 27 August 2009
Responsible department: Department of Mathematics

Entry requirements

120 credit points including Introduction to Partial Differential Equations

Learning outcomes

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

know the Ito-integral and how to use stochastic differential calculus;
know how to use Feynman - Kac's representation formula and the Kolmogrov equations;
know the theory for stochastic control, optimal stopping problems and free boundary problems;
be able to 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.