Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations

doi:10.1007/s10915-018-00896-w

	Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations
	Yang, Jie 1; Zhao, Weidong 2,3; Zhou, Tao4
	2019-06-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	79 期号:3 页码:1409-1432
摘要	This is the second part of our series papers on the deferred correction method for forward backward stochastic differential equations. In this work, we extend our previous work in Tang et al. (Numer Math Theory Methods Appl 10(2):222-242, 2017) to solve second-order forward backward stochastic differential equations (2FBSDEs). More precisely, we propose a class of explicit deferred correction schemes for 2FBSDEs. The key feature is that the simple Euler scheme is used as an initialization. Then, by a simple deferred correction iteration scheme, one can obtain an approximated solution with very high accuracy. Yet in each iteration, the computational complexity is always comparable to the Euler solver. Numerical examples are presented to show the effectiveness of the proposed scheme. We believe that the scheme proposed in this work is promising when dealing with 2FBSDEs in moderate dimensions.
关键词	Deferred correction method Second-order forward backward stochastic differential equations Euler scheme High-order rate of convergence
DOI	10.1007/s10915-018-00896-w
语种	英语
资助项目	science challenge Project[TZ2018001] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[91630203] ; NSF of China[11571351] ; NSF of China[11731006] ; NSF of China[11571206] ; NSF of China[11801320] ; national key basic research program[2018YFB0704304] ; NCMIS ; youth innovation promotion association (CAS) ; NSF of Shandong Province[ZR2018BA005]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000466934400003
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34839
专题	计算数学与科学工程计算研究所
通讯作者	Zhao, Weidong
作者单位	1.Shandong Univ, Sch Math & Stat, Weihai 264209, Shandong, Peoples R China 2.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China 3.Shandong Univ, Inst Finance, Jinan 250100, Shandong, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Yang, Jie,Zhao, Weidong,Zhou, Tao. Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,79(3):1409-1432.
APA	Yang, Jie,Zhao, Weidong,&Zhou, Tao.(2019).Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations.JOURNAL OF SCIENTIFIC COMPUTING,79(3),1409-1432.
MLA	Yang, Jie,et al."Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations".JOURNAL OF SCIENTIFIC COMPUTING 79.3(2019):1409-1432.