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

Abstract

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.

References in corpus (2)

• The Starting and Stopping Problem under Knightian Uncertainty and Related Systems of Reflected BSDEs
• Multi-dimensional BSDE with Oblique Reflection and Optimal Switching

Cited by in corpus (4)

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• On the Equality of Solutions of Max-Min and Min-Max Systems of Variational Inequalities with Interconnected Bilateral Obstacles
• Multidimensional dynamic risk measure via conditional g-expectation
• Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles of non-local type