We propose a novel mortality improvement model with the difference of death counts follows the Skellam distribution. We extend Mitchell et al. (2013) by considering the difference in Poisson death counts instead of the ratio of subsequent mortality rate, which does not have a known distribution. We derive the iterative estimators of the model from the Skellam distribution. Our model can employ maximum likelihood estimation for estimation issues such as missing data and provides a better fit than Mitchell et al. (2013). Using English and Wales mortality rate age 0-89 data during 1950-2016, the model estimate suggests that the age-dependent mortality improvement is slower than the benchmark, which coincides with a recent observation by Office for National Statistics (2018). The forecasting performance outperforms the Poisson and M10 model. We make inferences on the price of longevity swaps and analyze how the volatility shock of mortality improvement affects the premium of longevity swaps.

我们提出了一种新颖的死亡率改善模型，其死亡数的差异遵循Skellam分布。我们扩展了Mitchell等。（2013年）通过考虑泊松死亡率计数的差异而不是随后的死亡率比率（后者没有已知的分布）进行比较。我们从Skellam分布中得出模型的迭代估计量。我们的模型可以将最大似然估计用于估计问题，例如数据丢失，并提供比Mitchell等人更好的拟合度。（2013）。使用1950-2016年期间英国和威尔士的0-89岁死亡率数据，模型估计表明与年龄相关的死亡率改善速度低于基准值，这与国家统计局（2018）的最新观察结果相吻合。预测性能优于Poisson和M10模型。