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

2014/08/19 by Boualem Djehiche, Saïd Hamadène, Djehiche, Boualem +5 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #49L25 #49N70 #60H30 #90C39 #93E20 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1408.4282

openalex publication_date 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Viscosity Solutions of Systems of Variational Inequalities with\n Interconnected Bilateral Obstacles

Cited by

• An overview of unconstrained free boundary problems
• Zero-sum Stochastic Differential Games of Impulse Control with Random Intervention Costs

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