英文标题：
《An Aspect of Optimal Regression Design for LSMC》
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作者：
Christian Wei{\\ss}, Zoran Nikoli\\\'c
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最新提交年份：
2019
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英文摘要：
Practitioners sometimes suggest to use a combination of Sobol sequences and orthonormal polynomials when applying an LSMC algorithm for evaluation of option prices or in the context of risk capital calculation under the Solvency II regime. In this paper, we give a theoretical justification why good implementations of an LSMC algorithm should indeed combine these two features in order to assure numerical stability. Moreover, an explicit bound for the number of outer scenarios necessary to guarantee a prescribed degree of numerical stability is derived. We embed our observations into a coherent presentation of the theoretical background of LSMC in the insurance setting.
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中文摘要：
从业人员有时建议在使用LSMC算法评估期权价格或在Solvency II制度下的风险资本计算时，使用Sobol序列和正交多项式的组合。在本文中，我们从理论上证明了为什么LSMC算法的良好实现确实应该结合这两个特性以确保数值稳定性。此外，还导出了保证规定数值稳定性所需的外部场景数的显式界。我们将我们的观察结果嵌入到保险背景下LSMC理论背景的连贯呈现中。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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