Strong solutions of forward–backward stochastic differential equations with measurable coefficients

Peng Luo, Olivier Menoukeu-Pamen and Ludovic Tangpi

Stochastic Processes and their Applications, 2022, vol. 144, issue C, 1-22

Abstract: This paper investigates solvability of fully coupled systems of forward–backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to construct strong solutions. Despite the irregularity of the coefficients, the solutions turn out to be differentiable, at least in the Malliavin sense and, as functions of the initial variable, in the Sobolev sense.

Keywords: Singular PDEs; Sobolev regularity; FBSDE; Singular coefficients; Strong solutions; Malliavin calculus (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2021.10.012

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