Topics in Probability Theory and Stochastic Pro

BEA513 Topics in Probability Theory and Stochastic Pro

  • Topics

    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

    Learning outcome

    After completion of the course, the students should:

    Knowledge

    • have knowledge of 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.
    • be able to solve stochastic differential equations analytically as well as numerically and to compute conditional expectations based on filtered information.

    Skills

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

    General competence

    • have general competence in stochastic analysis and consider applications to problems in economics. Stochastic analysis is a prerequisite for many different topics in economics and management science, and is a must for studies in mathematical finance.

  • Teaching

    Teaching

    Regular lectures/exercises solved within group

  • Recommended prerequisites

    Recommended prerequisites

    As much mathematics as possible, particularly relevant are the courses MAT10 and 11.

  • Requirements for course approval

    Requirements for course approval

    Two compulsory assignments

  • Assessment

    Assessment

    Oral presentation of individual topic

  • Grading Scale

    Grading Scale

    Pass/Fail

  • Computer tools

    Computer tools

    Any suitable programming language

  • Semester

    Semester

    Autumn

  • Literature

    Literature

    Bernt Øksendal: Stochastic Differential Equations, Springer.

Overview

ECTS Credits
5
Teaching language
English
Semester
Autumn

Course responsible

Jan Ubøe, Dept of Business and Management Science