Robust Time-Inconsistent Stochastic Linear-Quadratic Control: An Open-Loop Approach

Abstract

This paper studies stochastic linear-quadratic control problems for an ambiguity-adverse agent with a time-inconsistent objective. We allow the agent to incorporate disturbances into the state's drift or choose an alternative model among a set of models equivalent to the reference model, to reflect her ambiguity aversion on the drift coefficient of the state process. We adopt an innovative two-step equilibrium control approach to characterize the robust time-consistent controls and simultaneously preserve the preference order. Under a general framework allowing random parameters, we derive a sufficient condition for equilibrium controls using the forward-backward stochastic differential equation approach. We also provide analytical solutions to mean-variance portfolio problems for various settings. Our empirical studies confirm the improvement in the portfolio's performance in terms of Sharpe ratio by incorporating robustness.