NDLI: Optimal Switching in Finite Horizon under State Constraints

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kharroubi, Idris
Copyright Year	2016
Abstract	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 one 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) 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.
Sponsorship	Agence Nationale de la Recherche
Starting Page	2202
Ending Page	2233
Page Count	32
File Format	PDF
ISSN	03630129
DOI	10.1137/15M1012281
e-ISSN	10957138
Issue Number	4
Volume Number	54
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-08-30
Access Restriction	Subscribed
Subject Keyword	energy and resources management Financial applications of other theories Optimal stochastic control Applications of stochastic analysis dynamic programming Stochastic ordinary differential equations state constraints optimal switching variational inequalities
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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