Robust Time-inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach

arXiv2306.16982MaRDI QIDQ6442003

Hoi Ying Wong, Bingyan Han, Chi Seng Pun

Publication date: 29 June 2023

Abstract: This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, under mild technical assumptions. To illustrate our framework, we consider two scenarios of robust mean-variance analysis, namely with state- and control-dependent ambiguity aversion. We find numerically that with time inconsistency haunting the dynamic optimal controls, the ambiguity aversion enhances the effective risk aversion faster than the linear, implying that the ambiguity in the TIC cases is more impactful than that under the TC counterparts, e.g., expected utility maximization problems.

Has companion code repository: https://github.com/hanbingyan/diffgame

Mathematics Subject Classification ID

Applications of optimal control and differential games (49N90) Applications of game theory (91A80) Stochastic games, stochastic differential games (91A15) Portfolio theory (91G10)

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