Semi-linear Backward Stochastic Integral Partial Differential Equations driven by a Brownian motion and a Poisson point process

2010/07/19 by Shaokuan Chen, Chen, Shaokuan, Shanjian Tang +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1007.3201

openalex publication_date 2010/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an Itô-Wentzell formula for jump diffusions as well as an abstract result of stochastic evolution equations, we obtain the stochastic integral partial differential equation for the inverse of the stochastic flow generated by a stochastic differential equation driven by a Brownian motion and a Poisson point process. By composing the random field generated by the solution of a backward stochastic differential equation with the inverse of the stochastic flow, we construct the classical solution of the system of backward stochastic integral partial differential equations. As a result, we establish a stochastic Feynman-Kac formula.

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• Backward Stochastic Riccati Equation with Jumps associated with Stochastic Linear Quadratic Optimal Control with Jumps and Random Coefficients
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