Uniqueness of Viscosity Solutions for Optimal Multi-Modes Switching Problem with Risk of default

TL;DR

This paper proves the uniqueness of viscosity solutions for a complex system of variational inequalities modeling optimal multi-modes switching with default risk, relevant for energy market applications.

Contribution

It establishes the uniqueness of solutions for a broad class of switching problems with polynomial growth costs and default risk, extending existing theory.

Findings

Proved uniqueness of solutions for the system of variational inequalities.

Extended the theory to polynomial growth cost functions.

Connected the mathematical model to power plant valuation.

Abstract

In this paper we study the optimal m-states switching problem in finite horizon as well as infinite horizon with risk of default. We allow the switching cost functionals and cost of default to be of polynomial growth and arbitrary. We show uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem with risk of default. This problem is connected with the valuation of a power plant in the energy market.