A unified approach to gradient type formulas for BSDEs and some applications

2021/03/11 by Xiliang Fan, Michael Röckner, Fan, Xiliang +3
Economics, Econometrics and Finance · Mathematics · #34F05 #60G22 #60H10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2103.06761

openalex publication_date 2021/03/11 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28

Abstract

In this paper we present a unified approach to establish gradient type formulas and Bismut type formulas for backward stochastic differential equations (BSDEs). This approach relies on a mix of derivative formulas with respect to the conditional probability of forward SDEs and the expression of the solution of BSDEs. Some concrete examples are given to illustrate the results. As applications, we provide representation formulas for the control solutions to McKean-Vlasov BSDEs and derive gradient estimates for related PDEs.

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