Speaker: Dr. Zhou Zhou received B.S. in Mathematics from Nankai University in 2010, and Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan in 2015. He was a Postdoctoral Fellow at the institute for Mathematics and its Applications in the University of Minnesota during 2015 - 2017. He joined the University of Sydney in 2018 and is now a Senior Lecturer of the School of Mathematics and Statistics. His research interests include mathematical finance, optimal stopping, stochastic control and games.

Date: October 16, 2024

Time: 10:00-11:00

Location: B924, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

When an optimal stopping problem involves non-exponential discounting, the problem is typically time-inconsistent. That is, an optimal stopping strategy derived today may no longer be optimal from a future’s perspective. A popular approach to address this time inconsistency is to use a game-theoretic framework and look for an equilibrium strategy: given the future selves use this strategy, the current self has no incentive to deviate. In this talk we will start with equilibrium strategies in discrete time under infinite time horizon. We obtain the existence of an equilibrium and an optimal one, an equilibrium that point wisely dominates other equilibria in terms of the associated value functions. Next, we will consider the problem in continuous time under infinite horizon. We will discuss different equilibrium concepts as well as their relation. Finally, we will talk about the case in continuous time under finite horizon. We propose a notion called almost strong equilibrium and establish its existence and uniqueness. We also investigate its convergence as the time horizon goes to infinity.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/195810.htm