BEA513 Topics in Probability Theory and Stochastic Processes
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
- Basic properties of Brownian motion
- Numerical simulation of Brownian motion
- Calculating expected values related to Brownian increments
- Filtrations and filtered information
- Stochastic integrals
- Numerical simulations of stochastic integrals
- The Ito formula
- Geometric Brownian motion
- The Ornstein-Uhlenbeck process
- Numerical schemes for stochastic differential equations
- Calculating conditional expectations
- Applications to continuous time newsvendor models
After completion of the course, the students:
- understand dynamic systems and be able to describe how and why systems change.
- 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.
- are able to address problems in stochastic analysis and its applications in economics.
Regular lectures/exercises solved within group.
PhD students at NHH have access to this course. Other (PhD and master's) students can be granted access by application if there is sufficient capacity.
The course requires a solid background in mathematics.
Two compulsory assignments
Oral presentation of individual topic.
Compulsory activities (work requirements) is valid for one semester after the semester it was obtained. Re-take is offered the semester after the course was offered for students with valid compulsory activities (work requirements).
Any suitable programming language
Bernt Øksendal: Stochastic Differential Equations, Springer.
- ECTS Credits
- Teaching language
Autumn. Offered Autumn 2022.
Jan Ubøe, Dept of Business and Management Science