Representation formulas for solutions of Isaacs integro-PDE

We prove suband super-optimality inequalities of dynamic programming for viscosity solutions of Isaacs integro-PDE associated with two-player, zero-sum stochastic differential game driven by a Levy type noise. This implies that the lower and upper value functions of the game satisfy the dynamic programming principle and they are the unique viscosity solutions of the lower and upper Isaacs integro-PDE. We show how to regularize viscosity suband super-solutions of Isaacs equations to smooth suband super-solutions of slightly perturbed equations.