Quasi-Monte Carlo for discontinous integrands with singularities along the boundary of the unit cube
Quasi-Monte Carlo for discontinous integrands with singularities along the boundary of the unit cube
复制标题
用于沿单位立方体边界具有奇点的不连续被积函数的拟蒙特卡罗
DOI：
10.1090/mcom/3324
复制
发表时间：
2018
影响因子：
2
通讯作者：
He Zhijian
中科院分区：
文献类型：
--
作者：
He Zhijian
本文研究了在单位立方体边界上具有沿着奇点的不连续被积函数的随机拟蒙特卡罗（QMC）抽样。在金融衍生品的定价和套期保值中，不连续性和奇异性是非常普遍的，它们对QMC的准确性有着巨大的影响。我们已经知道，随机QMC的均方根误差仅适用于具有奇异性的不连续函数。我们发现，在一定的条件下，随机QMC对任意小的值都有期望误差.此外，如果不连续面的边界平行于某些坐标轴，则可以获得更好的速率。作为一个副产品，我们发现，预期的错误率attainsif的不连续性是QMC友好的，在这个意义上，所有的不连续边界平行于坐标轴。研究结果可用于评估金融工程中一些典型问题的QMC精度。引用
This paper studies randomized quasi-Monte Carlo (QMC) sampling for discontinuous integrands having singularities along the boundary of the unit cube. Both discontinuities and singularities are extremely common in the pricing and hedging of financial derivatives and have a tremendous impact on the accuracy of QMC. It was previously known that the root mean square error of randomized QMC is onlyfor discontinuous functions with singularities. We find that under some mild conditions, randomized QMC yields an expected error offor arbitrarily small. Moreover, one can get a better rate if the boundary of discontinuities is parallel to some coordinate axes. As a by-product, we find that the expected error rate attainsif the discontinuities are QMC-friendly, in the sense that all the discontinuity boundaries are parallel to coordinate axes. The results can be used to assess the QMC accuracy for some typical problems from financial engineering. References