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

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.

36 pages

Cited by in corpus (3)

• Finite-horizon optimal multiple switching with signed switching costs
• Viscosity Solutions for a System of PDEs and Optimal Switching
• Viscosity solution of system of integro-partial differential equations with interconnected obstacles of non-local type without Monotonicity Conditions