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

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.(c) 2023 Elsevier B.V. All rights reserved.