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Pré-Publication, Document De Travail Année : 2022

Systems of PDEs with Interconnected Bilateral Obstacles and nonlinear Neumann Boundary Conditions

Résumé

In this article, we derive the existence and uniqueness of continuous viscosity solution of Bellman-Isaacs system of equations, associated with a multiple mode switching game in finite horizon when the state process is constrained to live in a connected bounded closed domain. We rely on systems of penalized reflected generalized BSDEs with unilateral obstacles, that provide approximation of the system of PDEs. We obtain a comparison result which gives the uniqueness and the continuity of the viscosity solution. This allows us to use Perron's method to obtain the existence.
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Dates et versions

hal-03603191 , version 1 (09-03-2022)

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  • HAL Id : hal-03603191 , version 1

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Manal Jakani. Systems of PDEs with Interconnected Bilateral Obstacles and nonlinear Neumann Boundary Conditions. 2022. ⟨hal-03603191⟩
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