The ranking of insurance risks with respect to their right tail is a challenging problem. In this paper, we extend the actuarial index introduced by Wang (1998) and propose its sensitivity index based on Leser’s perturbation analysis on a proportional hazards model. We use tail variability measures by conditioning the risk for values greater than the Value-at-Risk (VaR), and we study in detail how the VaR affects the actuarial and the sensitivity index. We provide characterization results for Pareto and exponential distributions, two cases where the actuarial and its sensitivity index are independent from VaR. We also obtain monotonicity results and bounds for them. The results are illustrated by numerical examples.

保险风险相对于其右尾的排名是一个具有挑战性的问题。在本文中，我们扩展了Wang（1998）引入的精算指数，并基于基于比例风险模型的Leser摄动分析，提出了其敏感性指数。我们通过调节风险值大于风险值（VaR）的风险来使用尾部变异性度量，并且我们详细研究了VaR如何影响精算和敏感性指数。我们提供了Pareto和指数分布的表征结果，这两种情况是精算师及其敏感性指数与VaR无关。我们还获得了单调性结果以及它们的界限。结果通过数值实例说明。