论文标题
多级蒙特卡洛，用于使用标准公式和其他应力测试计算SCR
Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests
论文作者
论文摘要
本文研究了多级蒙特卡罗估计量，以期最大程度地预期。当考虑许多应力测试时，自然会出现此问题，并出现在SCR标准公式的利率模块的计算中。我们获得了理论收敛的结果，可以补充Giles和Goda的最新工作，并通过以某种方式描述了最大值围绕最大值的规则性能，从而提供了一些额外的障碍。然后，我们将MLMC估计器应用于未来日期的SCR的计算，该日期使用ALM储蓄业务的标准公式在人寿保险上进行计算。我们将其与使用最不正方形的蒙特卡洛或神经网络获得的估计器进行了比较。我们发现，MLMC估计器在计算上更有效，并且具有避免回归问题的主要优势，这在保险公司由于路径依赖性而被保险公司投影的背景下尤为重要。最后，我们讨论了这种数值方法的潜力，并特别分析了投资组合分配对将来〜日期SCR的影响。
This paper studies the multilevel Monte-Carlo estimator for the expectation of a maximum of conditional expectations. This problem arises naturally when considering many stress tests and appears in the calculation of the interest rate module of the standard formula for the SCR. We obtain theoretical convergence results that complements the recent work of Giles and Goda and gives some additional tractability through a parameter that somehow describes regularity properties around the maximum. We then apply the MLMC estimator to the calculation of the SCR at future dates with the standard formula for an ALM savings business on life insurance. We compare it with estimators obtained with Least Square Monte-Carlo or Neural Networks. We find that the MLMC estimator is computationally more efficient and has the main advantage to avoid regression issues, which is particularly significant in the context of projection of a balance sheet by an insurer due to the path dependency. Last, we discuss the potentiality of this numerical method and analyze in particular the effect of the portfolio allocation on the SCR at future~dates.
