Two-player zero-sum stochastic differential games with random horizon. (December 2019)

• Record Type: Journal Article
• Authors: Ferreira, M.; Pinheiro, D.; Pinheiro, S.
• Is Part Of: Advances in applied probability. Volume 51:Number 4(2019)
• Page Start: 1209
• Page End: 1235
• Publication Date: 2019-12
• Subjects: stochastic differential game, -- dynamic programming, -- viscosity solutions; Primary 49N70, -- Secondary 91A15, -- 49L20, -- 49L25; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2019.47
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: We consider a two-player zero-sum stochastic differential game with a random planning horizon and diffusive state variable dynamics. The random planning horizon is a function of a non-negative continuous random variable, which is assumed to be independent of the Brownian motion driving the state variable dynamics. We study this game using a combination of dynamic programming and viscosity solution techniques. Under some mild assumptions, we prove that the value of the game exists and is the unique viscosity solution of a certain nonlinear partial differential equation of Hamilton–Jacobi–Bellman–Isaacs type.