Switching Game of Backward Stochastic Differential Equations and Associated System of Obliquely Reflected Backward Stochastic Differential Equations

Ying Hu (1) , Shanjian Tang (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 SCHOOL OF MATHEMATICAL SCIENCES - School of Mathematical Sciences

This paper is concerned with the switching game of a one-dimensional backward stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a system of matrix-valued BSDEs living in a special unbounded convex domain with reflection on the boundary along an oblique direction. In this paper, we show the existence of an adapted solution to this system of BSDEs with oblique reflection by the penalization method, the monotone convergence, and the a priori estimates.

Mots clés: Switching Game; backward stochastic differential equations; oblique reflection

Domaines: Probabilités [math.PR]

Ying Hu, Shanjian Tang. Switching Game of Backward Stochastic Differential Equations and Associated System of Obliquely Reflected Backward Stochastic Differential Equations. Discrete and Continuous Dynamical Systems - Series A, 2015, 35 (11), pp.5447-5465. ⟨10.3934/dcds.2015.35.5447⟩. ⟨hal-00287645v2⟩