MATJ5115 MA3: Optimal Stopping and Free-Boundary Problems (JSS32) (2 op)

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)

 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

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