Multilevel Monte Carlo simulation for Lévy processes based on the Wiener–Hopf factorisation
Multilevel Monte Carlo simulation for Lévy processes based on the Wiener–Hopf factorisation
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基于 Wiener-Hopf 分解的 Lévy 过程的多级蒙特卡洛模拟
DOI：
10.1016/j.spa.2013.09.015
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发表时间：
2012
影响因子：
1.4
通讯作者：
G. Suryanarayana
中科院分区：
文献类型：
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作者：
Albert Ferreiro;A. Kyprianou;Robert Scheichl;G. Suryanarayana
在Kuznetsov等人中。(2011)介绍了一种新的基于Wiener-Hopf分解的L过程的蒙特卡罗模拟技术。我们通过将他们的技术与最近引入的多水平蒙特卡罗方法相结合来进一步探索这一想法。此外，我们还首次对Kuznetsov等人提出的新的蒙特卡罗模拟技术进行了理论分析。(2011)及其多级变种，用于根据L过程的历史轨迹计算函数的期望值。我们推导了这两种方法的收敛速度，并证明了它们关于“跳跃活动”(例如，用Blumenthal-GToor指数刻画)是一致的。我们还在Kuznetsov等人中提出了该算法的修改版本。(2011)结合多水平方法得到了一般Lévy过程和Lipschitz泛函的最优收敛速度。这一最终结果目前只是一个理论上的结果，因为它需要从三个分布中独立抽样，而这目前只可能用于有限数量的过程。
In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Lévy processes that is based on the Wiener–Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced multilevel Monte Carlo methodology. Moreover, we provide here for the first time a theoretical analysis of the new Monte Carlo simulation technique in Kuznetsov et al. (2011) and of its multilevel variant for computing expectations of functions depending on the historical trajectory of a Lévy process. We derive rates of convergence for both methods and show that they are uniform with respect to the “jump activity” (e.g. characterised by the Blumenthal–Getoor index). We also present a modified version of the algorithm in Kuznetsov et al. (2011) which combined with the multilevel methodology obtains the optimal rate of convergence for general Lévy processes and Lipschitz functionals. This final result is only a theoretical one at present, since it requires independent sampling from a triple of distributions which is currently only possible for a limited number of processes.
影响因子：
2.7
作者：
Giles, Michael B.
通讯作者：
Giles, Michael B.
影响因子：
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作者：
Cliffe, K. A.;Giles, M. B.;Teckentrup, A. L.
通讯作者：
Teckentrup, A. L.