abstract:
We study multilevel Monte Carlo algorithms for Lévy-driven SDEs. More explicitly, we aim at computing the expectation $E[f(Y)]$, where $\{Y_{t}\}_{t\in[0,1]}$ is the solution of a stochastic differential equation driven by a Lévy process $\{X_{t}\}_{t\in[0,1]}$ and $f$ is a Lipschitz continuous function on path space.
Crucial for the computation is the simulation of the Lévy process and we combine a truncated shot noise representation with a direct simulation of the cumulated contribution of the remainder. Here the direct simulation of the remainder is established via inversion of the characteristic function. The new algorithms have worst case error of order $n^{-\frac{1}{2}}$ in the runtime $n$, even if the Blumenthal-Getoor Index $\beta$ is larger than 1. Our result improves previous research. |