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EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES
Fu, Yu1,2,3; Zhao, Weidong2,3; Zhou, Tao4
2017-11-01
Source PublicationDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
ISSN1531-3492
Volume22Issue:9Pages:3439-3458
AbstractThis 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.
KeywordSpectral method sparse grid approximations forward backward stochastic differential equations conditional expectations fast Fourier transform
DOI10.3934/dedsb.2017174
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000409963100011
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
Citation statistics
Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26566
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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