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

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.