We evaluate the performance of different approaches for estimating quantiles of compound distributions, which are widely used for risk quantification in the banking and insurance industries. We focus on three approaches: (1) single-loss approximation (SLA), (2) perturbative expansion correction (PEC) and (3) the fast Fourier transform (FFT). We demonstrate that both the SLA and PEC approaches are accurate only for tail quantiles of subexponential distributions. The PEC approach produces accurate estimates for quantiles greater than 95, while the SLA can only do this for quantiles greater than 99.9. Thus, the PEC approach dominates the SLA approach. The FFT approach consistently gives the most accurate estimates for every distribution. However, the FFT approach is substantially less time efficient than the PEC or SLA approaches, which are closed-form solutions. We contribute to the literature by providing practical guidance on selecting appropriate approaches for the various parametric distributions and quantiles used in the banking and insurance industries.

中文翻译：

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计算化合物分布的尾分位数

我们评估了估计复合分布分位数的不同方法的性能，这些方法广泛用于银行和保险业的风险量化。我们专注于三种方法：（1）单损失近似（SLA），（2）微扰扩展校正（PEC）和（3）快速傅立叶变换（FFT）。我们证明 SLA 和 PEC 方法仅对次指数分布的尾分位数是准确的。PEC 方法为大于 95 的分位数生成准确估计，而 SLA 只能对大于 99.9 的分位数执行此操作。因此，PEC 方法支配了 SLA 方法。FFT 方法始终如一地为每个分布提供最准确的估计。然而，FFT 方法的时间效率明显低于 PEC 或 SLA 方法，它们是封闭形式的解决方案。我们通过为银行和保险业中使用的各种参数分布和分位数选择合适的方法提供实用指导，为文献做出贡献。