Reflected Backward Stochastic Differential Equation with Jumps and Viscosity Solution of Second Order Integro-Differential Equation Without Monotonicity Condition: Case with the Measure of Lévy 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 the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy’s measure is infinite.