Convergence of numerical approximation for jump models involving delay and mean-reverting square root process

The mean-reverting square root process with jump has been widely used as a model on the financial market. Since the diffusion coefficient in the model does not satisfy the linear growth condition and local Lipschitz condition, we can not examine its properties by traditional techniques. To overcome the difficulties, we develop several new techniques to examine the numerical method of jump models involving delay and mean-reverting square root. We show that the numerical approximate solutions converge to the true solutions. Finally, we apply the convergence to examine a path-dependent option price and a bond in the financial pricing.