Time-Inconsistent Recursive Stochastic Optimal Control Problems

Keywords

Equilibrium Hamilton-Jacobi-Bellman equation; Equilibrium strategy; Stochastic differential games; Stochastic optimal control; Time-inconsistency

Abstract

A time-inconsistent stochastic optimal control problem with a recursive cost func- tional is studied. Equilibrium strategy is introduced, which is time-consistent and locally approxi- mately optimal. By means of multiperson hierarchical differential games associated with partitions of the time interval, a family of approximate equilibrium strategy is constructed, and by sending the mesh size of the time interval partition to zero, an equilibrium Hamilton{Jacobi{Bellman (HJB) equation is derived through which the equilibrium value function can be identified and the equilib- rium strategy can be obtained. Moreover, a well-posedness result of the equilibrium HJB equation is established under certain conditions, and a verification theorem is proved. Finally, an illustrative example is presented, and some comparisons of different definitions of equilibrium strategy are put in order.

Publication Date

1-1-2017

Publication Title

SIAM Journal on Control and Optimization

Volume

55

Issue

6

Number of Pages

4156-4201

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/16M1079415

Socpus ID

85039973316 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85039973316

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