Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

doi:10.4208/cicp.240515.280815a

	Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs
	Kong, Tao 1,2; Zhao, Weidong 1,2; Zhou, Tao3
	2015-11-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	18 期号:5 页码:1482-1503
摘要	In this paper, we are concerned with probabilistic high order numerical schemes for Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic PDEs, it is shown by Cheridito, Soner, Touzi and Victoir [4] that the associated exact solutions admit probabilistic interpretations, i.e., the solution of a fully nonlinear parabolic PDE solves a corresponding second order forward backward stochastic differential equation (2FBSDEs). Our numerical schemes rely on solving those 2FBSDEs, by extending our previous results [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci, Comput., 36 (2014), pp. A1731-A1751.]. Moreover, in our numerical schemes, one has the flexibility to choose the associated forward SDE, and a suitable choice can significantly reduce the computational complexity. Various numerical examples including the HJB equations are presented to show the effectiveness and accuracy of the proposed numerical schemes.
关键词	Fully nonlinear parabolic PDEs second order FBSDEs probabilistic interpretations probabilistic numerical schemes
DOI	10.4208/cicp.240515.280815a
语种	英语
资助项目	National Natural Science Foundations of China[91130003] ; National Natural Science Foundations of China[11201461] ; National Natural Science Foundations of China[11171189]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000365681400012
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21409
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, Finance Inst, 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	Kong, Tao,Zhao, Weidong,Zhou, Tao. Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2015,18(5):1482-1503.
APA	Kong, Tao,Zhao, Weidong,&Zhou, Tao.(2015).Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,18(5),1482-1503.
MLA	Kong, Tao,et al."Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 18.5(2015):1482-1503.