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1. Zero-sum Switching Game, Systems of Reflected Backward SDEs and Parabolic PDEs with bilateral interconnected obstacles

Author

Hamadène, Said, Mu, Tingshu, Laboratoire Manceau de Mathématiques (LMM), and Le Mans Université (UM)

Subjects
System of PDEs, Viscosity solution, Reflected Backward SDEs, Probability (math.PR), MathematicsofComputing_NUMERICALANALYSIS, 91A15, 35F21, HJB equations, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Perron's method AMS Classification subjects: 49L25, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Zero-sum switching game, FOS: Mathematics, Bilateral obstacles, Mathematics - Probability
Abstract

In this paper we study a zero-sum switching game and its verification theorems expressed in terms of either a system of Reflected Backward Stochastic Differential Equations (RBSDEs in short) with bilateral interconnected obstacles or a system of parabolic partial differential equations (PDEs in short) with bilateral interconnected obstacles as well. We show that each one of the systems has a unique solution. Then we show that the game has a value.

Published
2020

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