A stochastic target formulation for optimal switching problems in finite horizon

Bruno Bouchard (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LFA - Laboratoire de Finance Assurance

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 firm's valuation.

Mots clés: Optimal switching; impulse control; stochastic targets; jump diffusion processes; viscosity solutions; comparison principle

Domaines: Probabilités [math.PR]

Bruno Bouchard. A stochastic target formulation for optimal switching problems in finite horizon. Stochastics and Stochastics Reports, 2009, 81 (2), pp.171-197. ⟨hal-00090377⟩