Multilevel Path Simulation to Jump-Diffusion Process with Superlinear Drift

TL;DR

This paper demonstrates the strong convergence of multilevel Monte Carlo methods using specific Euler schemes for nonlinear jump-diffusion SDEs with certain Lipschitz conditions, supported by numerical experiments.

Contribution

It establishes theoretical convergence results for MLMC algorithms with SSBE and BE schemes in nonlinear jump-diffusion SDEs under relaxed Lipschitz conditions.

Findings

Strong convergence of MLMC with SSBE and BE schemes proven.

Numerical experiments confirm theoretical results.

Applicable to nonlinear jump-diffusion processes with specific Lipschitz conditions.

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.