A stochastic target formulation for optimal switching problems in finite horizon

Bouchard, Bruno

Bouchard, Bruno (2009), A stochastic target formulation for optimal switching problems in finite horizon, Stochastics, 81, 2, p. 171 - 197. http://dx.doi.org/10.1080/17442500802327360

Type

Article accepté pour publication ou publié

Date

2009-09-24

Journal name

Stochastics

Volume

Number

Publisher

Taylor & Francis

Pages

171 - 197

Abstract (EN)

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.

Subjects / Keywords

Viscosity solutions; Optimal Control