Optimal Switching in Finite Horizon under State Constraints

Idris Kharroubi (1, 2)

1 CREST - Centre de Recherche en Économie et Statistique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study an optimal switching problem with a state constraint: the controller is only allowed to choose strategies that keep the controlled diffusion in a closed domain. We prove that the value function associated to the weak formulation of this problem is the limit of the value function associated to an unconstrained switching problem with penalized coefficients, as the penalization parameter goes to infinity. This convergence allows to set a dynamic programming principle for the constrained switching problem. We then prove that the value function is a constrained viscosity solution to a system of variational inequalities (SVI for short). We finally prove that the value function is the maximal solution to this SVI. All our results are obtained without any regularity assumption on the constraint domain.

Mots clés: energy management; Optimal switching; state constraints; dynamic programming; variational in- equalities; energy management.

Domaines: Probabilités [math.PR]

Idris Kharroubi. Optimal Switching in Finite Horizon under State Constraints. 2014. ⟨hal-00990981v1⟩