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.
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}
}