Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps

doi:10.1007/s10915-016-0212-y

	Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps
	Fu, Yu 1,2; Zhao, Weidong 1,2; Zhou, Tao3
	2016-11-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	69 期号:2 页码:651-672
摘要	In this work, we are concerned with multistep schemes for solving forward backward stochastic differential equations with jumps. The proposed multistep schemes admit many advantages. First of all, motivated by the local property of jump diffusion processes, the Euler method is used to solve the associated forward stochastic differential equation with jump, which reduce dramatically the entire computational complexity, however, the quantities of interests in the backward stochastic differential equations (with jump) are still of high order rate of convergence. Secondly, in each time step, only one jump is involved in the computational procedure, which again reduces dramatically the computational complexity. Finally, the method applies easily to partial-integral differential equations (and some nonlocal PDE models), by using the generalized Feynman-Kac formula. Several numerical experiments are presented to demonstrate the effectiveness of the proposed multistep schemes.
关键词	Multistep scheme Jump-diffusion process Forward backward stochastic differential equation with jumps
DOI	10.1007/s10915-016-0212-y
语种	英语
资助项目	National Natural Science Foundations of China[11571206] ; National Natural Science Foundations of China[91530118] ; National Natural Science Foundations of China[11571351]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000385151700009
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/23962
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	1.Shandong Univ, Sch Math, Jinan 250100, Peoples R China 2.Shandong Univ, Inst Finance, Jinan 250100, Peoples R China 3.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	Fu, Yu,Zhao, Weidong,Zhou, Tao. Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps[J]. JOURNAL OF SCIENTIFIC COMPUTING,2016,69(2):651-672.
APA	Fu, Yu,Zhao, Weidong,&Zhou, Tao.(2016).Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps.JOURNAL OF SCIENTIFIC COMPUTING,69(2),651-672.
MLA	Fu, Yu,et al."Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps".JOURNAL OF SCIENTIFIC COMPUTING 69.2(2016):651-672.