Seminar

Department of Systems Engineering and Engineering Management

The Chinese University of Hong Kong

Title: Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time

Speaker: Prof. Yu-Jui Huang, University of Colorado

Abstract: A new definition of continuous-time equilibrium controls is investigated. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak equilibria" are coined for controls under the new and the standard definitions, respectively. When the state process is a time-homogeneous continuous-time Markov chain, a careful asymptotic analysis gives complete characterizations of weak and strong equilibria. Thanks to Kakutani-Fan's fixed-point theorem, general existence of weak and strong equilibria is also established, under additional compactness assumption. Our theoretic results are applied to a two-state model under non-exponential discounting. In particular, we demonstrate explicitly that there can be incentive to deviate from a weak equilibrium, which justifies the need for strong equilibria. Our analysis also provides new results for the existence and characterization of discrete-time equilibria under infinite horizon.

Biography: Yu-Jui Huang received B.B.A. in Finance and B.S. in Mathematics from National Taiwan University in 2007, and Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan in 2013. He was a lecturer in financial mathematics at the School of Mathematical Sciences at Dublin City University in Dublin, Ireland during 2013--2016, and joined the Department of Applied Mathematics at the University of Colorado at Boulder as an assistant professor in 2016. His research interests include mathematical finance, stochastic control, and optimal stopping. He has published a number of papers in leading journals, such as Annals of Applied Probability, SIAM Journal on Control and Optimization, and Finance and Stochastics. Currently, he is an associate editor of Proceedings of IEEE Conference on Decision and Control.