Survey on Path-Dependent PDEs

被引：0
|
作者：
Peng, Shige [1 ]
Song, Yongsheng [2 ,3 ]
Wang, Falei [1 ]
机构：
[1] Shandong Univ, Zhongtai Secur Inst Financial Studies, Sch Math, Jinan 250100, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2023年 / 44卷 / 06期
基金：
中国国家自然科学基金; 国家重点研发计划;
关键词：
Path-Dependent; Wiener expectation; BSDEs; Classical solution; Sobolev solution; Viscosity solution; OPTIMAL STOCHASTIC-CONTROL; NONLINEAR 2ND-ORDER EQUATIONS; G-BROWNIAN MOTION; VISCOSITY SOLUTIONS; DIFFERENTIAL-EQUATIONS; INFINITE DIMENSIONS; G-EXPECTATION; CALCULUS;
D O I：
10.1007/s11401-023-0048-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the authors provide a brief introduction of the path-dependent partial di.erential equations (PDEs for short) in the space of continuous paths, where the path derivatives are in the Dupire (rather than Frechet) sense. They present the connections between Wiener expectation, backward stochastic di.erential equations (BSDEs for short) and path-dependent PDEs. They also consider the well-posedness of path-dependent PDEs, including classical solutions, Sobolev solutions and viscosity solutions.
引用
收藏
页码：837 / 856
页数：20
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