The existence of value functions of stochastic differential games for unbounded stochastic evolution

Abstract

Considers a two-player, zero-sum stochastic differential game with unbounded dynamics in an infinite dimensional Hilbert space. The authors prove that the upper and lower value functions of the game are viscosity solutions of the upper and lower value Bellman-Isaacs equations respectively and that they satisfy the dynamic programming principle. It then follows that the differential game has value if the Isaacs condition holds.