Optimal Multi-Modes Switching Problem in Infinite Horizon

Abstract

This paper studies the problem of the deterministic version of the Verification Theorem for the optimal m-states switching in infinite horizon under Markovian framework with arbitrary switching cost functions. The problem is formulated as an extended impulse control problem and solved by means of probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differential equations. A viscosity solutions approach is employed to carry out a finne analysis on the associated system of m variational inequalities with inter-connected obstacles. We show that the vector of value functions of the optimal problem is the unique viscosity solution to the system. This problem is in relation with the valuation of firms in a financial market.

References in corpus (1)

• On the One-Dimensional Optimal Switching Problem

Cited by in corpus (4)

• A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation
• Deterministic Minimax Impulse Control in Finite Horizon: the Viscosity Solution Approach
• An Investment Model with Switching Costs and the Option to Abandon
• Uniqueness of Viscosity Solutions for Optimal Multi-Modes Switching Problem with Risk of default