Linear Quadratic Stochastic Two-Person Zero-Sum Differential Games In An Infinite Horizon

Keywords

Algebraic Riccati equation; Infinite horizon; Linear quadratic stochastic differential game; Open-loop and closed-loop saddle points; Stabilizing solution; Two-person; Zero-sum

Abstract

This paper is concerned with a linear quadratic stochastic two-person zero-sum differential game with constant coefficients in an infinite time horizon. Open-loop and closed-loop saddle points are introduced. The existence of closed-loop saddle points is characterized by the solvability of an algebraic Riccati equation with a certain stabilizing condition. A crucial result makes our approach work is the unique solvability of a class of linear backward stochastic differential equations in an infinite horizon.

Publication Date

7-1-2016

Publication Title

ESAIM - Control, Optimisation and Calculus of Variations

Volume

22

Issue

3

Number of Pages

743-769

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1051/cocv/2015024

Socpus ID

84977138765 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84977138765

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