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 firm's valuation.