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Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality

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Abstract

We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex (time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    TianYang Nie

  2. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    TianYang Nie

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  1. TianYang Nie
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Nie, T. Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality. Sci. China Math. 58, 729–748 (2015). https://doi.org/10.1007/s11425-014-4887-y

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