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

TL;DR

This paper introduces a novel approach to viscosity solutions of integro-partial differential equations by leveraging the concavity of the generator, establishing existence and uniqueness even with finite Lévy measures.

Contribution

It presents a new method connecting BSDEs with jumps to viscosity solutions of IPDEs using concavity, expanding applicability to cases with finite Lévy measures.

Findings

Established existence and uniqueness of solutions using concavity.

Extended the theory to cases with finite Lévy measures.

Linked BSDEs with jumps to viscosity solutions of IPDEs.

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.