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.
Keywords: Stochastic switching diffusion, time-inconsistency, stochastic optimal control, equilibrium strategy, Hamilton–Jacobi–Bellman equation
Mei, Hongwei 1 ; Yong, Jiongmin 1
@article{COCV_2019__25__A64_0,
author = {Mei, Hongwei and Yong, Jiongmin},
title = {Equilibrium strategies for time-inconsistent stochastic switching systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2019},
publisher = {EDP Sciences},
volume = {25},
doi = {10.1051/cocv/2018051},
zbl = {1441.93346},
mrnumber = {4023125},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2018051/}
}
TY - JOUR AU - Mei, Hongwei AU - Yong, Jiongmin TI - Equilibrium strategies for time-inconsistent stochastic switching systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2018051/ DO - 10.1051/cocv/2018051 LA - en ID - COCV_2019__25__A64_0 ER -
%0 Journal Article %A Mei, Hongwei %A Yong, Jiongmin %T Equilibrium strategies for time-inconsistent stochastic switching systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2018051/ %R 10.1051/cocv/2018051 %G en %F COCV_2019__25__A64_0
Mei, Hongwei; Yong, Jiongmin. Equilibrium strategies for time-inconsistent stochastic switching systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 64. doi: 10.1051/cocv/2018051
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