Volume 25, 2019
|Number of page(s)||60|
|Published online||25 October 2019|
Equilibrium strategies for time-inconsistent stochastic switching systems*
Department of Mathematics, The University of Kansas,
KS 66045, USA.
2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA.
** Corresponding author: firstname.lastname@example.org
Accepted: 18 September 2018
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.
Mathematics Subject Classification: 93E20 / 49N70 / 60G07
Key words: Stochastic switching diffusion / time-inconsistency / stochastic optimal control / equilibrium strategy / Hamilton–Jacobi–Bellman equation
© EDP Sciences, SMAI 2019
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