A number of stochastic mortality models with transitory jump effects have been proposed for the securitization of catastrophic mortality risks. Most of the studies on catastrophic mortality risk modeling assumed that the mortality jumps occur once a year or used a Poisson process for their jump frequencies. Although the timing and the frequency of catastrophic events are unknown, the history of the events might provide information about their future occurrences. In this paper, we propose a specification of the Lee–Carter model by using the renewal process and we assume that the mean time between jump arrivals is no longer constant. Our aim is to find a more realistic mortality model by incorporating the history of catastrophic events. We illustrate the proposed model with mortality data from the US, the UK, Switzerland, France, and Italy. Our proposed model fits the historical data better than the other jump models for all countries. Furthermore, we price hypothetical mortality bonds and show that the renewal process has a significant impact on the estimated prices.

已经提出了许多具有瞬时跳跃效应的随机死亡率模型，用于对灾难性死亡风险进行证券化。关于灾难性死亡风险建模的大多数研究都假设死亡率每年发生一次跳跃，或者使用Poisson过程确定其跳跃频率。尽管灾难性事件的发生时间和频率未知，但事件的历史可能会提供有关其将来发生的信息。在本文中，我们通过更新过程提出了Lee-Carter模型的规范，并假设跳跃到达之间的平均时间不再恒定。我们的目标是通过合并灾难性事件的历史来找到更现实的死亡率模型。我们用来自美国，英国，瑞士，法国和意大利的死亡率数据说明了该模型。我们提出的模型比所有国家/地区的其他跳跃模型都更适合历史数据。此外，我们对假设的死亡率债券进行定价，并表明更新过程对估计价格有重大影响。