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

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

2012-02-06

arxiv.org/abs/1202.1108v1

Mathematics

Optimization and Control

25 pages; Real options, Backward stochastic differential equations, Snell envelope, Stopping times, Switching, Viscosity solut

Scientific paper

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.

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