基于Milstein离散化的多级蒙特卡洛路径模拟分析
Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation
AI总结：
本文分析采用Milstein离散化的多级蒙特卡洛路径模拟效率，证明其可提升多级估计量的方差收敛阶，并通过篮子期权数值结果验证分析的实用性。
摘要：
Giles于2008年在《Operations Research》第56卷第3期607-617页提出的多级蒙特卡洛路径模拟方法，利用强收敛特性，结合不同分辨率的模拟以降低计算复杂度。本文分析该方法采用Milstein离散化时的效率；Milstein离散化相比标准Euler-Maruyama方法具有更高的强收敛阶，本文证明这会使多级估计量的方差收敛阶得到提升。文中还给出了篮子期权的数值结果，以说明该分析的实用性。
英文摘要：
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milstein discretisation; this has an improved order of strong convergence compared to the standard Euler-Maruyama method, and it is proved that this leads to an improved order of convergence of the variance of the multilevel estimator. Numerical results are also given for basket options to illustrate the relevance of the analysis.
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