Bismut-Elworthy-Li Formulae for Forward-Backward SDEs with Jumps and Applications

2025/12/29 by Jiagang Ren, Hua Zhang, Ren, Jiagang +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.2512.23288

Abstract

Under nondegeneracy assumptions on the diffusion coefficients, we establish the derivative formulae of Bismut-Elworthy-Li's type for forward-backward stochastic differential equations with respect to Poisson random measure using the lent particle method created by Bouleau and Denis, which is not given before. Applying this formula, the existence and uniqueness of a solution of nonlocal quasi-linear integral partial differential equations, which are differentiable with respect to the space variable, are obtained, even if the initial datum and coefficients of this equation are not.

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