Robust equilibrium strategies for time-inconsistent stochastic optimal control problems with applications

Abstract

In this paper, a new robust time-inconsistent stochastic optimal control problem is investigated under a general jump-diffusion model. Such a problem can be described as a sup-sup-inf problem consisting of the optimal control and the optimal selection of a probability measure that reflects the optimistic and pessimistic sentiments of the agent. Under a game-theoretic framework, the definition of the equilibrium control-measure strategy is given for the robust time-inconsistent stochastic optimal control problem and then an extended Hamilton–Jacobi–Bellman–Isaacs (HJBI) system and a verification theorem are derived for characterizing the equilibrium control-measure strategy and the corresponding equilibrium value function. Moreover, some financial optimization problems and numerical experiments are provided to illustrate the applicability of our newly derived results.