Reflected backward stochastic differentialequation with jumps and viscosity solution of second order integro-differential equation without monotonicity condition: case with the measure of Levy infinite

Abstract

We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show existence and uniqueness of a continuous viscosity solution of equation with non local terms, in case the generator is not monotonous and Levy's measure is infinite.