Syllabus for Partial Differential Equations with Applications to Finance

Partiella differentialekvationer med finansiella tillämpningar

  • 5 credits
  • Course code: 1MA255
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Mathematics A1N, Financial Mathematics A1N
  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2009-03-12
  • Established by:
  • Revised: 2018-08-30
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 24, 2019
  • Entry requirements: 120 credits including 90 credits in mathematics. English 6.
  • Responsible department: Department of 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.

On completion of the course, 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 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.

Reading list

The reading list is missing. For further information, please contact the responsible department.