Master’s studies

Syllabus for Partial Differential Equations with Applications to Finance

Partiella differentialekvationer med finansiella tillämpningar

Syllabus

  • 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), 3, 4, 5.
  • Established: 2009-03-12
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2013-04-23
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 34, 2013
  • Entry requirements: 120 credits including 90 credits in mathematics.
  • 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.

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

Reading list

Applies from: week 30, 2013

Robert Kohn: PDE for Finance, Spring 2011. Electronic textbook which can be accessed at http://www.math.nyu.edu/faculty/kohn/pde_finance_2011.html