A proposition of generalized stochastic Milevsky–Promislov mortality models

Abstract

The aim of this article is to propose a new approach to the estimation of the mortality rates based on two extended Milevsky and Promislov models: the first one with colored excitations modeled by Gaussian linear filters and the second one with excitations modeled by a continuous non-Gaussian process. The exact analytical formulas for theoretical mortality rates based on Gaussian linear scalar filter models have been derived. The theoretical values obtained in both cases were compared with theoretical mortality rates based on a classical Lee–Carter model, and verified on the basis of empirical Polish mortality data. The obtained results confirm the usefulness of the switched model based on the continuous non-Gaussian process for modeling mortality rates.

Keywords:

• Forecasting of mortality rates
• hybrid mortality models
• switched models
• Lee–Carter model
• Ito stochastic differential equations

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors thank PL-Grid Infrastructure for the use of computing power. This research was supported in part by PL-Grid Infrastructure [PLGPS2016a].