Viscosity solutions of systems of PDEs with interconnected obstacles and switching problem without monotonicity condition

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.

System of Nonlinear Second-Order Parabolic Partial Differential Equations with Interconnected Obstacles and Oblique Derivative Boundary Conditions on Non-Smooth Time-Dependent Domains

“…Later on, Chassagneux, Elie and Kharroubi [5] proved the existence of a unique solution for the system of reflected BSDEs without the monotonicity assumption on the function f . Then, the related PDEs system with interconnected obstacles has been investigated by Hamadene, Mnif and Neffati [11], where a unique continuous viscosity solution has been provided without the monotonicity condition. Afterwards, when the diffusion is required to stay in a bounded time-independent domain, the switching problem has been considered by Boufoussi, Hamadene and Jakani [1].…”