Topics in Probability Theory and Stochastic Processes

BEA513 Topics in Probability Theory and Stochastic Processes

  • Topics


    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

    Learning outcome

    After completion of the course, the students should be able to


    1. The students should have knowledge on dynamical 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.
    2. solve stochastic differential equations analytically as well as numerically and to compute conditional expectations based on filtered information.


    1. compute stochastic integrals, analytically by use of the Ito formula, and numerically via the Euler and Milstein schemes.
    2. handle explicit formulas for geometric Brownian motion and the Ornstein-Uhlenbeck process, and to apply this theory to practical problems.

    General competence

    The course provides general competence in stochastic analysis and consider applications of the theory to problems in economics. The theory is a prerequisite for many different topics in economics and management science, and is a must for studies in mathematical finance.

  • Teaching


    Regular lectures/exercises solved within group

  • Recommended prerequisites

    Recommended prerequisites

    As much mathematics as possible

  • Requirements for course approval

    Requirements for course approval

    Two compulsory assignments

  • Assessment


    Oral presentation of individual topic

  • Grading Scale

    Grading Scale


  • Computer tools

    Computer tools

    Any suitable programming language

  • Semester



  • Literature


    Bernt Øksendal: Stochastic Differential Equations, Springer.


ECTS Credits
Teaching language

Course responsible

Jan Ubøe, Dept of Business and Management Science