# Viscosity solution of system of integro-partial differential equations with interconnected obstacles of non-local type without Monotonicity Conditions

## TL;DR

This paper develops a new approach to solving systems of integro-partial differential equations with interconnected obstacles and non-local terms, removing the need for monotonicity conditions, and proves existence and uniqueness of viscosity solutions.

## Contribution

It introduces a method to construct unique viscosity solutions for complex integro-PDE systems without monotonicity assumptions, using reflected backward stochastic differential equations with jumps.

## Key findings

- Established existence of solutions for the system.
- Proved uniqueness of the viscosity solution.
- Extended the theory to non-monotone generators.

## Abstract

In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution which is unique in the class of functions with polynomial growth. In our study, the main tool is the notion of reflected backward stochastic differential equations with jumps with interconnected obstacles for which we show the existence of a solution.