Equilibrium Strategies for Time-Inconsistent Stochastic Switching Systems
Abstract
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is time-inconsistent in general. Therefore, instead of finding a global optimal control (which is not possible), we look for a time-consistent (approximately) locally optimal equilibrium strategy. Such a strategy can be represented through the solution to a system of partial differential equations, called an equilibrium Hamilton-Jacob-Bellman (HJB, for short) equation which is constructed via a sequence of multi-person differential games. A verification theorem is proved and, under proper conditions, the well-posedness of the equilibrium HJB equation is established as well.
Cite
@article{arxiv.1712.09505,
title = {Equilibrium Strategies for Time-Inconsistent Stochastic Switching Systems},
author = {Hongwei Mei and Jiongmin Yong},
journal= {arXiv preprint arXiv:1712.09505},
year = {2017}
}