Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion

doi:10.1016/j.spa.2019.07.014

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	Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion
	Hong, Jialin 1,2; Huang, Chuying 1,2; Kamrani, Minoo 3; Wang, Xu 1,2
	2020-05-01
发表期刊	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN	0304-4149
卷号	130 期号:5 页码:2675-2692
摘要	In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox-Ingersoll-Ross model driven by fractional Brownian motion with Hurst parameter H is an element of (1/2, 1). To deal with the difficulties caused by the unbounded diffusion coefficient, we study an auxiliary equation based on Lamperti transformation. By means of Malliavin calculus, we prove that the backward Euler scheme applied to this auxiliary equation ensures the positivity of the numerical solution, and is of strong order one. Furthermore, a numerical approximation for the original model is obtained and converges with the same order. (C) 2019 Elsevier B.V. All rights reserved.
关键词	Cox-Ingersoll-Ross model Fractional Brownian motion Backward Euler scheme Optimal strong convergence rate Malliavin calculus
DOI	10.1016/j.spa.2019.07.014
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[11290142]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000528486200004
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51346
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Chuying
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Razi Univ, Fac Sci, Dept Math, Kermanshah, Iran
推荐引用方式 GB/T 7714	Hong, Jialin,Huang, Chuying,Kamrani, Minoo,et al. Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2020,130(5):2675-2692.
APA	Hong, Jialin,Huang, Chuying,Kamrani, Minoo,&Wang, Xu.(2020).Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,130(5),2675-2692.
MLA	Hong, Jialin,et al."Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130.5(2020):2675-2692.