IUMJ

Title: Representation formulas for solutions of Isaacs integro-PDE

Authors: Shigeaki Koike and Andrzej Swiech

Issue: Volume 62 (2013), Issue 5, 1473-1502

Abstract:

We prove sub- and 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 L\'evy-type noise. This implies that the lower and upper value functions of the game satisfy the dynamic programming principle and that they are the unique viscosity solutions of the lower and upper Isaacs integro-PDE. We show how to regularize viscosity sub- and super-solutions of Isaacs equations to smooth sub- and super-solutions of slightly perturbed equations.