A stochastic target formulation for optimal switching problems in finite horizon

Abstract

We consider a general optimal switching problem for a controlled diffusion and show that its value coincides with the value of a well-suited stochastic target problem associated to a diffusion with jumps. The proof consists in showing that the Hamilton–Jacobi–Bellman equations of both problems are the same and in proving a comparison principle for this equation. This provides a new family of lower bounds for the optimal switching problem, which can be computed by Monte-Carlo methods. This result has also a nice economical interpretation in terms of a firm's valuation.

Keywords:

• optimal switching
• impulse control
• stochastic targets
• jump diffusion processes
• viscosity solutions
• comparison principle

MSC Classification (2000):

• 62L15
• 49L25
• 49L20