English

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

Optimization and Control 2020-08-18 v2

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.

Keywords

Cite

@article{arxiv.2008.05582,
  title  = {A PDE approach for open-loop equilibriums in time-inconsistent stochastic optimal control problems},
  author = {Ishak Alia},
  journal= {arXiv preprint arXiv:2008.05582},
  year   = {2020}
}
R2 v1 2026-06-23T17:49:12.539Z