A PDE approach for open-loop equilibriums in time-inconsistent stochastic optimal control problems

Abstract

This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward stochastic differential equations with jumps (FBSDEJs, for short), we derive two systems of integro-partial differential equations (IPDEs, for short). Then, we rigorously prove a verification theorem which provides a sufficient condition for open-loop equilibrium strategies. As an illustration of the general theory, we discuss a mean-variance portfolio selection problem under a jump-diffusion model.

References in corpus (7)

• A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem
• On time-inconsistent stopping problems and mixed strategy stopping times
• Equilibrium policies when preferences are time inconsistent
• Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems
• A regular equilibrium solves the extended HJB system
• Equilibrium for Time-Inconsistent Stochastic Linear--Quadratic Control under Constraint
• Time-Inconsistent Stochastic Optimal Control Problems and Backward Stochastic Volterra Integral Equations