DEEP SIGNATURE FBSDE ALGORITHM

被引：5

作者：

Feng, Q., I ^{[1
]}

Luo, M. A. N. ^{[2
]}

Zhang, Z. H. A. O. Y. U. ^{[3
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Guotai Junan, Rd 655,Xinzha Rd,Bohua Plaza, Shanghai 200071, Peoples R China

[3] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2023年 / 13卷 / 3-4期

关键词：

Forward-backward stochastic differential equations; signature; recurrent neural network; option pricing;

D O I：

10.3934/naco.2022028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a deep signature/log-signature FBSDE algorithm to solve forward-backward stochastic differential equations (FBSDEs) with state and path dependent features. By incorporating the deep signature/log-signature transformation into the recurrent neural network (RNN) model, our algorithm shortens the training time, improves the accuracy, and extends the time horizon comparing to methods in the existing literature. Moreover, our algorithms can be applied to a wide range of applications such as state and path dependent option pricing involving high-frequency data, model ambiguity, and stochastic games, which are linked to parabolic partial differential equations (PDEs), and path-dependent PDEs (PPDEs). Lastly, we also derive the convergence analysis of the deep signature/log-signature FBSDE algorithm.

引用

页码：500 / 522

页数：23

共 33 条

[11]

Friz P. K., 2010, Multidimensional stochastic processes as rough paths: theory and applications

[12] APPROXIMATION OF DYNAMICAL-SYSTEMS BY CONTINUOUS-TIME RECURRENT NEURAL NETWORKS [J].