Robust Time-Inconsistent Stochastic Control Problems

This paper establishes a general analytical framework for continuous-time time-inconsistent stochastic control problems for ambiguity-averse agent, who is not confident in the reference model of the state process and... [ view full abstract ]

This paper establishes a general analytical framework for continuous-time time-inconsistent stochastic control problems for ambiguity-averse agent, who is not confident in the reference model of the state process and rather considers similar alternative models. We adopt a game-theoretic framework to derive an extended dynamic programming equation and extended Hamilton--Jacobi--Bellman--Isaacs equations for characterizing the robust dynamically optimal control of the problem. We also prove a verification theorem to theoretically support our construction of robust control. To illustrate the tractability, we study an example of robust dynamic mean-variance portfolio selection under two cases: 1. constant risk aversion; and 2. state-dependent risk aversion.