Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE

Finance and Stochastics Pub Date : 2022-06-11 DOI:10.1080/17442508.2022.2085503

Yufeng Shi, Jiaqiang Wen, J. Xiong

引用次数: 0

Abstract

In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional Itô (or path-dependent) calculus, the relationship between the systems and related path-dependent quasi-linear stochastic partial differential equations (SPDEs in short) is established, and the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Relat. Fields 98 (1994), pp. 209–227.] is developed to the non-Markovian situation. Moreover, we obtain the differentiability of the solution to the forward-backward doubly stochastic systems and some properties of solutions to the path-dependent SPDEs.

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正反向双随机系统及路径相关随机偏微分方程经典解

研究了一类非马尔可夫正反向双随机系统。利用泛函Itô(或路径相关)微积分技术，建立了系统与相关路径相关的拟线性随机偏微分方程(简称SPDEs)之间的关系，并建立了Pardoux和Peng[后向双随机微分方程和拟线性SPDEs系统，Probab]的著名非线性随机Feynman-Kac公式。代数理论。Fields 98(1994)，第209-227页。发展到非马尔可夫情况。此外，我们还得到了正反向双随机系统解的可微性，以及路径相关spde解的一些性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.