This article models the dynamics of age-specific incremental mortality as a stochastic process in which the drift rate can be simply and effectively modeled as the average annual improvement rate of a group time trend for all ages and the distribution of residuals can be fitted by one of the Gaussian distribution and four non-Gaussian distributions (Student t, jump diffusion, variance gamma, and normal inverse Gaussian). We use the one-factor copula model with six distributions for the factors (normal–normal, normal–Student t, Student t–normal, Student t–Student t, skewed t–normal, and skewed t–Student t) to capture the inter-age mortality dependence. We then construct three annuity portfolios (Barbell, Ladder, and Bullet) with equal portfolio value (total net single premium) and portfolio mortality duration but different portfolio mortality convexities. Finally, we apply our model to managing longevity risk by an approximation to the change in the portfolio value in response to a proportional or constant change in the force of mortality, and by estimating Value at Risk for the three annuity portfolios.

本文采用随机过程来模拟特定年龄段的死亡率的动态变化，其中漂移率可以简单有效地建模为所有年龄段的群体时间趋势的年平均增长率，残差的分布可以拟合一个高斯分布和四个非高斯分布（学生t，跳跃扩散，方差伽玛和正态逆高斯分布）的分布。我们用六个分布的一个因素Copula模型的因素（正常-正常，正常的-学生牛逼，学生牛逼-正常，学生牛逼-学生牛逼，歪斜牛逼-正常和扭曲牛逼-学生ŧ）以捕获年龄之间的死亡率依赖性。然后，我们构建三个年金投资组合（杠铃，阶梯和子弹），它们具有相等的投资组合价值（净净总保费）和投资组合死亡率持续时间，但投资组合死亡率凸度不同。最后，我们将模型应用于管理寿命风险，方法是根据死亡率的比例或恒定变化对投资组合价值的变化进行近似估算，并估算三个年金投资组合的风险价值。