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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2016

Optimal Switching in Finite Horizon under State Constraints

Résumé

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 with this problem is the limit of value functions associated with unconstrained switching problems 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 solution to a system of variational inequalities (SVI for short) in the constrained viscosity sense. We finally prove that uniqueness for our SVI cannot hold and we give a weaker characterization of the value function as the maximal solution to this SVI. All our results are obtained without any regularity assumption on the constraint domain.
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Dates et versions

hal-00990981 , version 1 (14-05-2014)
hal-00990981 , version 2 (06-03-2015)
hal-00990981 , version 3 (11-03-2015)
hal-00990981 , version 4 (07-06-2016)

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Citer

Idris Kharroubi. Optimal Switching in Finite Horizon under State Constraints. SIAM Journal on Control and Optimization, 2016, 54 (4), pp.2202-2233. ⟨hal-00990981v4⟩
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