Equilibrium strategies for time-inconsistent stochastic switching systems

被引：15
作者：
Mei H. [1 ]
Yong J. [2 ]
机构：
[1] Department of Mathematics, University of Kansas, Lawrence, 66045, KS
[2] Department of Mathematics, University of Central Florida, Orlando, 32816, FL
来源：
ESAIM - Control, Optimisation and Calculus of Variations | 2019年 / 25卷
关键词：
Equilibrium strategy; Hamilton-Jacobi-Bellman equation; Stochastic optimal control; Stochastic switching diffusion; Time-inconsistency;
D O I：
10.1051/cocv/2018051
中图分类号：
学科分类号：
摘要：
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) 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. © EDP Sciences, SMAI 2019.
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