Another method of viscosity solutions of integro-differential partial equation by concavity

Abstract: In this paper we consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) via the solution of backward stochastic differential equations(BSDE in short) with jumps where L\'evy's measure is not necessarily infinite. We mainly use the concavity of the generator at the level of its second variable to establish the existence and uniqueness of the solution with non local terms.