In this paper, we give a short and simple proof of the recent result of Ceng et al. (Math Methods Oper Res 67(3):375–390, 2008 ). Copyright Springer-Verlag 2011

In financial modelling, filtering and other areas the underlying dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, there is a need for the systematic...

This paper constructs strong discrete time approximations for pure jump processes that can be described by stochastic differential equations. Strong approximations based on jump-adapted time discretizations, which produce no discretization bias, are analyzed. The computational complexity of...

When using an Euler discretisation to simulate a mean-reverting square root process, one runs into the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this...

This paper introduces a new class of numerical schemes for the pathwise approximation of solutions of stochastic differential equations (SDEs). The proposed family of strong predictor-corrector Euler methods are designed to handle scenario simulation of solutions of SDEs. It has the potential to...

The paper introduces an approach for the derivation of discrete time approximations for solutions of stochastic differential equations with time delay. The suggested approximations converge in a strong sense. Furthermore, explicit solutions for linear stochastic delay equations are given.

Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result....

Using an Euler discretization to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretization is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case...