The Cox-Ingersoll-Ross model with delay and strong convergence of its Euler-Maruyama approximate solutions

被引：31

作者：

Wu, Fuke ^{[1
]}

Mao, Xuerong ^{[2
]}

Chen, Kan ^{[2
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Univ Strathclyde, Dept Stat & Modelling Sci, Glasgow G1 1XH, Lanark, Scotland

来源：

APPLIED NUMERICAL MATHEMATICS | 2009年 / 59卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Stochastic delay differential equation (SDDE); Strong convergence; EM method; TERM INTEREST-RATE; STOCHASTIC VOLATILITY; DIFFERENTIAL-EQUATIONS; INTEREST-RATES; STOCK RETURNS;

D O I：

10.1016/j.apnum.2009.03.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Stochastic delay differential equations (SDDEs) have recently been developed to model various financial quantities. In general, SDDEs have no explicit solution, so numerical methods for approximations have become one of the most powerful techniques in the Valuation of financial quantities. In this paper, we will concentrate on the Euter-Maruyama (EM) scheme for Cox-Ingersoll-Ross model with delay, whose diffusion coefficient is nonlinear and non-Lipschitz continuous such that some standard results cannot be appealed. We prove existence of the nonnegative solution and the strong convergence of its EM approximate solution. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：2641 / 2658

页数：18

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