Title
Equilibrium concepts for time-inconsistent stopping problems in continuous time
Abstract
In this talk, we study the new notion of equilibrium, which we call strong equilibrium and is introduced for time-inconsistent stopping problems in continuous time in the joint work with Erhan Bayraktar and Zhou Zhou in 2020. Compared to the previously established notions in Time-consistent stopping under decreasing impatience (Huang, Y.-J., & Nguyen-Huu, A. 2018. Finance and Stochastics, 22(1), 69–95) and On finding equilibrium stopping times for time-inconsistent markovian problems (Christensen, S., & Lindensjö, K. 2018. SIAM Journal on Control and Optimization, 56(6), 4228–4255), which in this paper are called mild equilibrium and weak equilibrium, respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log subadditive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence.
Bio
Jingjie Zhang is an assistant professor in China School of Banking and Finance at the University of International Business and Economics (UIBE). She received a Ph.D in Applied and Interdisciplinary Mathematics from the University of Michigan in 2021 under the supervision of Erhan Bayraktar and Indrajit Mitra, and a bachelor’s degree in Mathematics and Applied Mathematics from the University of Science and Technology of China in 2016. Jingjie’s research interests include stochastic control, game theory and their applications in finance and economics.