Problem
Research questions and friction points this paper is trying to address.
Study robust time-inconsistent stochastic control problems
Derive conditions for Nash equilibrium in games
Analyze ambiguity aversion in mean-variance scenarios
Robust Time-inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach
🤖 AI Summary
This paper addresses the robust linear-quadratic stochastic control problem under coupled model uncertainty (ambiguity aversion) and time-inconsistent preferences. Methodologically, it formulates—within a stochastic differential game framework—the first joint model of time-inconsistent preferences and state- and control-dependent ambiguity structures, and derives sufficient conditions for Nash equilibria via impulse variational methods, yielding time-consistent robust strategies. Theoretically, existence of such equilibria is established. Numerical results reveal that, under time inconsistency, ambiguity aversion induces a superlinear amplification of risk aversion, with its regulatory intensity markedly exceeding that of conventional time-consistent robust control paradigms. This work breaks the classical time-consistency assumption in robust control, providing a novel paradigm for modeling dual uncertainties—both parametric ambiguity and intertemporal preference inconsistency—in dynamic decision-making.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses stochastic differential game approach
Applies spike variation for Nash equilibrium
Analyzes robust mean-variance scenarios
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