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Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

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Type
Preprint
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Submission Date
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DOI: 10.1007/s00245-012-9184-y
arXiv ID: 1104.2689
Source
arXiv
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Abstract

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.

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