Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem |
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Authors: | S. Hamadène M. A. Morlais |
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Affiliation: | 1. LMM, Université du Maine, Avenue Olivier Messiaen, 72085, Le Mans, Cedex 9, France
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Abstract: | This paper deals with existence and uniqueness of a solution in viscosity sense, for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case is the Hamilton-Jacobi-Bellmann system of the Markovian stochastic optimal m-states switching problem. The switching cost functions depend on (t,x). The main tool is the notion of systems of reflected backward stochastic differential equations with oblique reflection. |
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