Mixed Zero-Sum Stochastic Differential Game and Doubly Reflected BSDEs with a Specific Generator

Brahim El Asri; Nacer Ourkiya

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arXiv · 2103.03134

Mixed Zero-Sum Stochastic Differential Game and Doubly Reflected BSDEs with a Specific Generator

Brahim El Asri·Nacer Ourkiya

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Abstract

This paper studies the mixed zero-sum stochastic differential game problem. We allow the functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. We show the existence of solution for this doubly reflected BSDEs and we prove the existence of a saddle-point of the game. Moreover, in the Markovian framework we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation.

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BibTeX RIS

Brahim El Asri, Nacer Ourkiya. 2021-03-04. Mixed Zero-Sum Stochastic Differential Game and Doubly Reflected BSDEs with a Specific Generator. https://arxiv.org/abs/2103.03134

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