Consider an insurer who both sells catastrophe insurance policies and makes risky investments. Suppose that insurance claims arrive according to a Poisson process and the price of the investment portfolio evolves according to a general stochastic process independent of the insurance claims. In the focus of catastrophe risk management are catastrophe insurance losses. For the case of heavy-tailed claims, we derive a simple asymptotic formula for the tail probability of the present value of future claims. The transparent expression of our formula explicitly reflects the different roles of the various underlying risks in driving catastrophic losses. Our work is distinguished from most other works in this strand of research in that we carry out the asymptotic study over the whole class of subexponential distributions. Thus, our work allows both very heavy-tailed distributions such as Pareto-type distributions and moderately heavy-tailed distributions such as Lognormal and Weibull distributions.

考虑一家既销售巨灾保险又进行风险投资的保险公司。假设保险索赔根据泊松过程到达，并且投资组合的价格根据独立于保险索赔的一般随机过程演变。巨灾风险管理的重点是巨灾保险损失。对于重尾债权的情况，我们推导出未来债权现值尾部概率的简单渐近公式。我们的公式的透明表达明确地反映了各种潜在风险在导致灾难性损失中的不同作用。我们的工作与这方面研究中的大多数其他工作不同，因为我们对整个次指数分布类别进行渐近研究。因此，