| Contents |
| We will present 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 they are the unique viscosity solutions of the lower and upper Isaacs integro-PDE. The method uses PDE techniques and is based on regularization of viscosity sub- and super-solutions of Isaacs equations to smooth sub- and super-solutions of slightly perturbed equations, and approximate optimal synthesis. It is constructive and provides a fairly explicit way to produce almost optimal controls and strategies. |
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