abstract:
In this talk, we consider multilevel Monte Carlo for the computation of expectations $E[f(Y)]$. Here $\{Y_{t}\}_{t\in[0,T]}$ denotes the solution to a L\'evy-driven stochastic differential equation and $f$ is at least Lipschitz continuous on path space. Approximate solutions are gained via the Euler method from an approximate simulation of the underlying L\'evy process.
We establish convergence rates and show a central limit theorem (similar to recent work of Ben Alay \& Kebaier for diffusions). The central limit theorem is based on a proof of stable convergence for the error for two successive levels. |