Asymptotically optimal allocation of stratified sampling with adaptive variance reduction by strata
Asymptotically optimal allocation of stratified sampling with adaptive variance reduction by strata
复制标题
DOI：
10.1145/1734222.1734225
复制
发表时间：
2010-04
期刊：
影响因子：
--
通讯作者：
Ray Kawai
中科院分区：
文献类型：
--
作者：
Ray Kawai
为了提高Monte Carlo模拟的效率，我们开发了一种自适应分层抽样算法，用于分配每个层内的抽样努力，其中应用了自适应方差减小技术。给定每个批次中的重复次数，我们的算法更新分配分数以最小化平均值的分层估计的工作归一化方差。当批次数趋于无穷大时，我们建立了均值的分层估计的渐近正态性。虽然所提出的算法的实施需要少量的初始工作，该算法有可能产生的估计效率的大幅提高。同样重要的是，自适应框架避免了需要频繁的重新校准的方差减少方法的参数应用在每一层内发生变化时，在实验条件控制系统的性能。为了说明我们算法的适用性和有效性，我们给出了一个Black-Scholes期权定价的数值结果，其中我们将潜在的布朗运动关于其终值分层，并将重要性抽样方法应用于填充在布朗路径中的正态随机变量，相对于按比例分配的估计方差，所提出的算法实现了估计方差的四倍减小，而计算时间的增加可以忽略不计。
To enhance efficiency in Monte Carlo simulations, we develop an adaptive stratified sampling algorithm for allocation of sampling effort within each stratum, in which an adaptive variance reduction technique is applied. Given the number of replications in each batch, our algorithm updates allocation fractions to minimize the work-normalized variance of the stratified estimator of the mean. We establish the asymptotic normality of the stratified estimator of the mean as the number of batches tends to infinity. Although implementation of the proposed algorithm requires a small amount of initial work, the algorithm has the potential to yield substantial improvements in estimator efficiency. Equally important is that the adaptive framework avoids the need for frequent recalibration of the parameters of the variance reduction methods applied within each stratum when changes occur in the experimental conditions governing system performance. To illustrate the applicability and effectiveness of our algorithm, we provide numerical results for a Black--Scholes option pricing, where we stratify the underlying Brownian motion with respect to its terminal value and apply an importance sampling method to normal random variables filling in the Brownian path. Relative to the estimator variance with proportional allocation, the proposed algorithm achieved a fourfold reduction in estimator variance with a negligible increase in computing time.