MULTILEVEL MONTE CARLO FOR LEVY-DRIVEN SDEs: CENTRAL LIMIT THEOREMS FOR ADAPTIVE EULER SCHEMES

• 成果类型: Article
• 署名作者: Dereich, Steffen; Li, Sangmeng
• 署名单位: University of Munster
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1087
• 发表日期: 2016
• 页码: 136-185
• 关键词: approximations

摘要

In this article, we consider multilevel Monte Carlo for the numerical computation of expectations for stochastic differential equations driven by Levy processes. The underlying numerical schemes are based on jump adapted Euler schemes. We prove stable convergence of an idealised scheme. Further, we deduce limit theorems for certain classes of functionals depending on the whole trajectory of the process. In particular, we allow dependence on marginals, integral averages and the supremum of the process. The idealised scheme is related to two practically implementable schemes and corresponding central limit theorems are given. In all cases, we obtain errors of order N-1/2 (log N)(1/2) in the computational time N which is the same order as obtained in the classical set-up analysed by Giles [Oper. Res. 56 (2008) 607-617]. Finally, we use the central limit theorems to optimise the parameters of the multilevel scheme.