EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES

doi:10.3934/dedsb.2017174

	EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES
	Fu, Yu 1,2,3; Zhao, Weidong 2,3; Zhou, Tao4
	2017-11-01
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
ISSN	1531-3492
卷号	22 期号:9 页码:3439-3458
摘要	This is the second part of a series papers on multi-step schemes for solving coupled forward backward stochastic differential equations (FBSDEs). We extend the basic idea in our former paper [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve high-dimensional FBSDEs, by using the spectral sparse grid approximations. The main issue for solving high-dimensional FBSDEs is to build an efficient spatial discretization, and deal with the related high-dimensional conditional expectations and interpolations. In this work, we propose the sparse grid spatial discretization. The sparse grid Gaussian-Hermite quadrature rule is used to approximate the conditional expectations. And for the associated high-dimensional interpolations, we adopt a spectral expansion of functions in polynomial spaces with respect to the spatial variables, and use the sparse grid approximations to recover the expansion coefficients. The FFT algorithm is used to speed up the recovery procedure, and the entire algorithm admits efficient and highly accurate approximations in high dimensions. Several numerical examples are presented to demonstrate the efficiency of the proposed methods.
关键词	Spectral method sparse grid approximations forward backward stochastic differential equations conditional expectations fast Fourier transform
DOI	10.3934/dedsb.2017174
语种	英语
资助项目	National Natural Science Foundations of China[91630312] ; National Natural Science Foundations of China[91630203] ; National Natural Science Foundations of China[11571351] ; National Natural Science Foundations of China[11171189] ; National Natural Science Foundations of China[11571206] ; NCMIS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000409963100011
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26566
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 Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, 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	Fu, Yu,Zhao, Weidong,Zhou, Tao. EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2017,22(9):3439-3458.
APA	Fu, Yu,Zhao, Weidong,&Zhou, Tao.(2017).EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,22(9),3439-3458.
MLA	Fu, Yu,et al."EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 22.9(2017):3439-3458.