On the Equality of Solutions of Max-Min and Min-Max Systems of Variational Inequalities with Interconnected Bilateral Obstacles

Boualem Djehiche; Said Hamadène; Marie-Amélie Morlais; Xuzhe Zhao

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arXiv · 1408.4282

On the Equality of Solutions of Max-Min and Min-Max Systems of Variational Inequalities with Interconnected Bilateral Obstacles

Boualem Djehiche·Said Hamadène·Marie-Amélie Morlais·Xuzhe Zhao

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Abstract

In this paper, we deal with the solutions of systems of PDEs with bilateral inter-connected obstacles of min-max and max-min types. These systems arise naturally in stochastic switching zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min-max and max-min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the the values of a zero-sum switching game is studied.

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Boualem Djehiche, Said Hamadène, Marie-Amélie Morlais, Xuzhe Zhao. 2014-08-19. On the Equality of Solutions of Max-Min and Min-Max Systems of Variational Inequalities with Interconnected Bilateral Obstacles. https://arxiv.org/abs/1408.4282

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