Two-player zero-sum stochastic differential games with regime switching. (April 2020)

• Record Type: Journal Article
• Authors: Lv, Siyu
• Is Part Of: Automatica. Volume 114(2020)
• Publication Date: 2020-04
• Subjects: Stochastic differential games -- Markov chains -- Dynamic programming principle -- HJBI equations -- Viscosity solutions; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.108819
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper is concerned with the two-player zero-sum stochastic differential game in a regime switching model with an infinite horizon. The state of the system is characterized by a number of diffusions coupled by a continuous-time finite-state Markov chain. Based on the dynamic programming principle (DPP), the lower and upper value functions are shown to be the unique viscosity solutions of the associated lower and upper Hamilton–Jacobi–Bellman–Isaacs (HJBI) equations, respectively. Moreover, the lower and upper value functions coincide under the Isaacs' condition, which implies that the game admits a value. All the proofs in this paper are markedly different from those for the case when there is no regime switching.