کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1156829 | 958879 | 2011 | 23 صفحه PDF | دانلود رایگان |
This article introduces and analyzes multilevel Monte Carlo schemes for the evaluation of the expectation E[f(Y)]E[f(Y)], where Y=(Yt)t∈[0,1]Y=(Yt)t∈[0,1] is a solution of a stochastic differential equation driven by a Lévy process. Upper bounds are provided for the worst case error over the class of all path dependent measurable functions ff, which are Lipschitz continuous with respect to the supremum norm. In the case where the Blumenthal–Getoor index of the driving process is smaller than one, one obtains convergence rates of order 1/n, when the computational cost nn tends to infinity. This rate is optimal up to logarithms in the case where YY is itself a Lévy process. Furthermore, an error estimate for Blumenthal–Getoor indices larger than one is included together with results of numerical experiments.
Journal: Stochastic Processes and their Applications - Volume 121, Issue 7, July 2011, Pages 1565–1587