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

Brahim El Asri () and Nacer Ourkiya ()
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Brahim El Asri: ENSA
Nacer Ourkiya: ENSA

Dynamic Games and Applications, 2024, vol. 14, issue 3, No 2, 549-577

Abstract: 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 (HJB) equation.

Keywords: Reflected backward stochastic differential equations; Mixed stochastic control; Control-stopping problem; Hamilton–Jacobi–Bellman equation; Viscosity solution; 93E20; 49J40; 49L25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-023-00515-w

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