Numerical methods for a class of jump–diffusion systems with random magnitudes

Abstract

Stochastic differential delay equations with Poisson driven jumps of random magnitude are popular as models in mathematical finance. In this paper, we shall deal with convergence of the semi-implicit Euler method for nonlinear stochastic differential delay equations with random jump magnitudes and show that the approximate solutions strongly converge to the exact solutions with the order 1 − 1/ q ( q > 1). This result is more general than what they deal with the jump of deterministic magnitude.