Systems of Integro-PDEs with Interconnected Obstacles and Multi-Modes Switching Problem Driven by Lévy Process

Abstract

In this paper we show existence and uniqueness of the solution in viscosity sense for a system of nonlinear $m$ variational integral-partial differential equations with interconnected obstacles whose coefficients $(f_i{)}_{i=1,\cdots ,m}$ depend on $(u_j{)}_{j=1,\cdots ,m}$. From the probabilistic point of view, this system is related to optimal stochastic switching problem when the noise is driven by a Lévy process. The switching costs depend on $(t,x)$. As a by-product of the main result we obtain that the value function of the switching problem is continuous and unique solution of its associated Hamilton-Jacobi-Bellman system of equations. The main tool we used is the notion of systems of reflected BSDEs with oblique reflection driven by a Lévy process.

41 pages

References in corpus (1)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited

Cited by in corpus (1)

• Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles of non-local type