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

TL;DR

This paper establishes the existence and uniqueness of viscosity solutions for a class of integro-partial differential equations with jumps, without requiring monotonicity, using reflected backward stochastic differential equations with infinite Levy measures.

Contribution

It extends the theory of viscosity solutions to non-monotonic generators with infinite Levy measures via RBSDEs with jumps.

Findings

Proved existence of viscosity solutions for non-monotonic generators.

Established uniqueness of solutions in the infinite Levy measure case.

Connected RBSDEs with jumps to viscosity solutions of IPDEs.

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.