Multi-dimensional BSDE with oblique reflection and optimal switching

By Ying Hu, Shanjian Tang. 2007

162 citations recorded by the source corpus.

In this paper, we study a multi-dimensional backward stochastic differential equation (BSDE) with oblique reflection, which is a BSDE reflected on the boundary of a special unbounded convex domain along an oblique direction, and which arises naturally in the study of optimal switching problem. The existence of the adapted solution is obtained by the penalization method, the monotone convergence, and the a priori estimates. The uniqueness is obtained by a verification method (the first component of any adapted solution is shown to be the vector value of a switching problem for BSDEs). As applications, we apply the above results to solve the optimal switching problem for stochastic differential equations of functional type, and we give also a probabilistic interpretation of the viscosity solution to a system of variational inequalities.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/211fb2cba567a8d24c7f97dca3e690ed6516dc93

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Citations in the corpus

A note on existence and uniqueness for solutions of multidimensional reflected BSDEs (2011, methodology): “This is done via the introduction of a convenient one dimensional dominating BSDE and the use of a standard comparison theorem.”
The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach (2008, background): “Either a probabilistic one ([10, 11, 17, 19, 22, 23]) or an approach which uses partial differential inequalities (PDIs for short) ([1, 2, 5, 13, 20, 29, 26]).”