BEA513 Topics in Probability Theory and Stochastic Processes

• Topics

  This course is an introductory course in stochastic analysis and focuses on developing students’ knowledge and understanding of dynamic systems. Static models generally fail to explain changes in the economy, and the time development of dynamical systems is crucial to understand how and why systems change. Geometric Brownian motion and the Ornstein-Uhlenbeck process are widely used in applications of this theory, and the students should be familiar with the construction of these processes. The part of stochastic analysis covered in this course, is a prerequisite for many different topics in economics and management science, and is a must for studies in mathematical finance

  Topics covered:

  1. Basic properties of Brownian motion
  2. Numerical simulation of Brownian motion
  3. Calculating expected values related to Brownian increments
  4. Filtrations and filtered information
  5. Stochastic integrals
  6. Numerical simulations of stochastic integrals
  7. The Ito formula
  8. Geometric Brownian motion
  9. The Ornstein-Uhlenbeck process
  10. Numerical schemes for stochastic differential equations
  11. Calculating conditional expectations
  12. Applications to continuous time newsvendor models

• Learning outcome

  After completion of the course, the students:

  Knowledge

  • Understand dynamic systems and be able to describe how and why systems change.

  Skills

  • Are able to compute stochastic integrals, analytically by use of the Ito formula, and numerically via the Euler and Milstein schemes.
  • Are able to solve stochastic differential equations analytically as well as numerically and to compute conditional expectations based on filtered information.
  • Are able to use geometric Brownian motions and the Ornstein-Uhlenbeck processes.

  General competence

  • Are able to address problems in stochastic analysis and its applications in economics.

• Teaching

  Regular lectures/exercises solved within group.

• Restricted access

  • PhD candidates at NHH.
  • PhD candidates at Norwegian institutions.
  • Motivated master student's at NHH may be admitted after application, but are subject to the approval from the course responsible on a case by case basis.

  For more information about the application process, please visit our webpage: https://www.nhh.no/en/study-programmes/phd-programme-at-nhh/phd-courses/become-a-visiting-student-at-a- phd-course-at-nhh/ (copy link).

• Recommended prerequisites

  The course requires a solid background in mathematics.

• Compulsory Activity

  Two compulsory assignments.

  Compulsory activities (work requirements) is valid for one semester after the semester it was obtained.

• Assessment

  Individual oral presentation of assigned topic.

  Re-take is offered the semester after the course was offered for students with valid compulsory activities (work requirements).

• Grading Scale

  Pass/Fail

• Computer tools

  Any suitable programming language (e.g. Maple, Mathematica, MatLab, ...)

• Literature

  Bernt Øksendal: Stochastic Differential Equations, Springer.