Modeling trend processes in parametric mortality models

作者：Boerger Matthias; Schupp Johannes^*

来源：Insurance: Mathematics and Economics , 2018, 78: 369-380.

DOI：10.1016/j.insmatheco.2017.09.024

• Longevity risk
• Mortality projection
• Parametric mortality models
• Mortality trend process
• Parameter uncertainty

Parametric mortality models like those of Lee and Carter (1992), Cairns et al. (2006), or Plat (2009) typically include one or more time dependent parameters. Often, a random walk with drift is used to project these parameters into the future. However, longer time series of historical mortality data often show patterns which a random walk with drift is highly unlikely to generate. In fact, historical mortality trends often appear to be trend stationary around piecewise linear trends with changing slopes over time (see, e.g., Sweeting (2011) or Li et al. (2011)). Periods of lower (but rather constant) mortality improvements are followed by periods of higher improvements and vice versa.
In this paper, we propose an alternative trend process which builds on the patterns observed in the historical data. Future trend changes occur randomly over time, and also the trend change magnitude is stochastic. Furthermore, we show how the parameters of this trend process, in particular the probability of observing a trend change in a certain year and the distribution for the trend change magnitude, can be estimated from historical data. We also outline how uncertainty in the parameter estimates can be accounted for. Finally, we compare the trend process to other trend processes which have been proposed in the literature.

• 出版日期2018-1