Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

TL;DR

This paper establishes existence and uniqueness of viscosity solutions for interconnected systems of PDEs, with applications to energy market valuation and power plant switching, using reflected BSDEs with oblique reflection.

Contribution

It introduces a framework for solving interconnected PDE systems with arbitrary switching costs, extending previous results to more general energy market models.

Findings

Proves existence and uniqueness of viscosity solutions for the system.

Connects the PDE system to reflected BSDEs with oblique reflection.

Applies results to valuation problems in energy markets.

Abstract

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.