In the context of life insurance with profit participation, the future discretionary benefits ($FDB$), which are a central item for Solvency~II reporting, are generally calculated by computationally expensive Monte Carlo algorithms. We derive analytic formulas to estimate lower and upper bounds for the $FDB$. This yields an estimation interval for the $FDB$, and the average of lower and upper bound is a simple estimator. These formulae are designed for real world applications, and we compare the results to publicly available reporting data.

翻译：在有利润参与的人寿保险方面,未来自由裁量福利(FDB$)是SOLENET-II报告的一个中心项目,通常通过计算昂贵的蒙特卡洛算法计算,我们得出分析公式来估计美元FDB$的下限和上限,得出美元FDB$的估计间隔,下限和上限的平均值是一个简单的估计数字。这些公式是为真实世界应用设计的,我们将结果与公开的报告数据进行比较。