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

Authors:
Fuke Wu;Xuerong Mao;Kan Chen
Affiliations:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UK;Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UK
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

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 Euler-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.