MATJ5115 MA3: Optimal Stopping and Free-Boundary Problems (JSS32) (2 cr)
Study level:
Postgraduate studies
Grading scale:
Pass - fail
Language:
English
Responsible organisation:
Faculty of Mathematics and Science
Curriculum periods:
2023-2024
Description
The lectures will disclose a fascinating connection between optimal stopping problems in probability and free-boundary problems in analysis. The focus will be on explaining the key concepts and principles through examples.
The topics to be covered and linked to free-boundary problems include:
- Optimal stopping problems
- Optimal prediction problems
- Nonlinear optimal stopping problems
- Quickest detection problems
- Optimal stopping games
References:
- Peskir, G. and Shiryaev, A. N. (2006). Optimal stopping and free-boundary problems. Lectures in Mathematics, ETH Zurich, Birkhauser, Basel (500 pp)
- Various research articles (2006-2023)
Learning outcomes
On successful completion of the course, the student will know
- what an optimal stopping problem (OSP) is
- how to classify OSPs
- how to establish a one-to-one correspondence between a given OSP and a free-boundary problem (FBP)
- how to solve a FBP
- how to verify that a solution to FBP is the sought solution to OSP
- how to make use of the derived solutions in various theoretical and applied settings
Description of prerequisites
In addition to being familiar with basic probability and analysis concepts, some knowledge of
- Markov processes (Brownian motion & Poisson process)
- Martingales (optional sampling theorem)
- Stochastic calculus (Ito's formula) will be helpful although not necessary
Completion methods
Method 1
Description:
Lectures and exercises
Evaluation criteria:
Pass/fail. Minimum attendance of 80% at lectures.
Select all marked parts
Parts of the completion methods
x
Participation in teaching (2 cr)
Type:
Participation in teaching
Grading scale:
Pass - fail
Language:
English