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Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems (1104.2689v2)
Published 14 Apr 2011 in math.OC and cs.SY
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.