Risk assessment on a stochastic basis has become prevalent in financial reporting due to increasingly sophisticated regulatory requirements. Many applications require nested stochastic projections, for which crude Monte Carlo can be too costly and time-consuming to perform to reach a reasonable degree of accuracy. While there has been ample literature on nested simulation methods in the area of portfolio management, less is known in the literature regarding nested simulation for financial reporting and internal risk management. There has been little research dealing with unique challenges arising from the structure of insurance liabilities. This paper intends to fill the gap in the literature by providing an overview of the use of nested stochastic modeling for different regulatory purposes and investigating the multi-period nested stochastic model, common in insurance products. The paper reviews a variety of so-called ‘stochastic-on-stochastic’ methods to speed up nested simulations. In addition, the paper presents a new hybrid ‘deterministic-on-stochastic’ method based on partial differential equation (PDE). To the best knowledge of the authors, this is the first time that a PDE method has been introduced for the purpose of nested stochastic projection. A numerical example is provided to show the high efficiency of the hybrid PDE method in a multi-period nested model for financial reporting.

由于日益复杂的监管要求，随机基础上的风险评估在财务报告中变得普遍。许多应用程序需要嵌套的随机投影，为此，原始蒙特卡罗可能过于昂贵和耗时，无法达到合理的准确度。虽然在投资组合管理领域有大量关于嵌套模拟方法的文献，但关于财务报告和内部风险管理的嵌套模拟的文献却知之甚少。很少有研究涉及保险负债结构带来的独特挑战。本文旨在通过概述嵌套随机模型用于不同监管目的并研究保险产品中常见的多周期嵌套随机模型来填补文献中的空白。该论文回顾了各种所谓的“随机对随机”方法来加速嵌套模拟。此外，本文提出了一种新的基于偏微分方程 (PDE) 的“确定性-随机性”混合方法。据作者所知，这是首次引入 PDE 方法用于嵌套随机投影。提供了一个数值例子来说明混合 PDE 方法在用于财务报告的多期嵌套模型中的高效率。该论文回顾了各种所谓的“随机对随机”方法来加速嵌套模拟。此外，本文提出了一种新的基于偏微分方程 (PDE) 的“确定性-随机性”混合方法。据作者所知，这是首次引入 PDE 方法用于嵌套随机投影。提供了一个数值例子来说明混合 PDE 方法在用于财务报告的多期嵌套模型中的高效率。该论文回顾了各种所谓的“随机对随机”方法来加速嵌套模拟。此外，本文提出了一种新的基于偏微分方程 (PDE) 的“确定性-随机性”混合方法。据作者所知，这是首次引入 PDE 方法用于嵌套随机投影。提供了一个数值例子来说明混合 PDE 方法在用于财务报告的多期嵌套模型中的高效率。