Ergodicity of robust switching control and nonlinear system of quasi variational inequalitiesReport as inadecuate




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1 Department of Mathematics, University of Michigan Department of Mathematics, University of Michigan 2 Dipartimento di Matematica, Politecnico di Milano Dipartimento di Matematica -F. Brioschi- 3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 4 CREST - Centre de Recherche en Économie et Statistique

Abstract : We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control problems introduced in 3. We prove that, as time horizon goes to infinity resp. discount factor goes to zero the long run average solution to the parabolic system resp. the limiting discounted solution to the elliptic system is characterized by a solution of a nonlinear system of ergodic variational inequalities. Our results hold under a dissipativity condition and without any non degeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments and in particular a dual randomized game representation for the solution to the system of variational inequalities.

Keywords : stochastic games ergodic problem randomization system of quasi variational inequalities Optimal switching





Author: Erhan Bayraktar - Andrea Cosso - Huyên Pham -

Source: https://hal.archives-ouvertes.fr/



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