Forward‐backward doubly stochastic differential equations with random jumps and related games

Abstract

AbstractA type of forward‐backward doubly stochastic differential equations driven by Brownian motions and the Poisson process (FBDSDEP) is studied. Under some monotonicity assumptions, the existence and uniqueness results for measurable solutions of FBDSDEP are established via a method of continuation. Then the continuity and differentiability of the solutions to FBDSDEP depending on parameters is discussed. Furthermore, these results were applied to backward doubly stochastic linear quadratic (LQ) nonzero sum differential games with random jumps to get the explicit form of the open‐loop Nash equilibrium point by the solution of the FBDSDEP.