# Partial Differential Equations with Applications to Finance

5 credits

Syllabus, Master's level, 1MA255

Code
1MA255
Education cycle
Second cycle
Main field(s) of study and in-depth level
Financial Mathematics A1N, Mathematics A1N
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 31 January 2024
Responsible department
Department of Mathematics

## Entry requirements

120 credits including 90 credits in mathematics. Financial Derivatives. Participation in Probability Theory II or Integration Theory. Proficiency in English equivalent to the Swedish upper secondary course English 6.

## Learning outcomes

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

On completion of the course, the student should be able to:

• give an account of the Ito-integral, stochastic differential calculus, and diffusion processes and use stochastic differential calculus in related problems;
• give an account of the heat equation, connection between stochastic differential equations and partial differential equations, and use Feynman - Kac's representation formula, Dynkin's formula, and the Kolmogorov equations in related problems;
• give an account of the theory for stochastic control, optimal stopping problems and free boundary problems, and use these to solve simple optimization problems;
• apply the theory to financial problems;

## Content

Stochastic calculus and diffusion processes. The heat equation, Feynman - Kac's representation formula and Dynkin's formula. The Kolmogorov equations. Stochastic control theory, optimal stopping problems and free boundary problems. Applications of the theory in finance and other related problems.

## Instruction

Lectures and problem solving sessions.

## Assessment

Written examination at the end of the course combined with assignments given during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.