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

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