Multilevel Path Simulation to Jump-Diffusion Process with Superlinear Drift

Abstract

In this work, we will show strong convergence of the Multilevel Monte-Carlo (MLMC) algorithm with split-step backward Euler (SSBE) and backward (drift-implicit) Euler (BE) schemes for nonlinear jump-diffusion stochastic differential equations (SDEs) when the coefficient drift is globally one-sided Lipschitz and the test function is only locally Lipschitz. We also confirm these theoretical results by numerical experiments for the jump-diffusion processes.