Gompertz Law Revisited: Forecasting Mortality with a Multi-factor Exponential Model

29 Pages Posted: 16 Dec 2019 Last revised: 12 Jan 2021

See all articles by Hong Li

Hong Li

Warren Centre for Actuarial Studies and Research, University of Manitoba

Ken Seng Tan

University of Waterloo

Shripad Tuljapurkar

Stanford University

Wenjun Zhu

Nanyang Business School, Nanyang Technological University

Date Written: December 31, 2019

Abstract

This paper provides a flexible multi-factor framework to address some ongoing challenges in mortality modeling, with a special focus on the mortality curvature and possible mortality plateau for extremely old ages. We extend the Gompertz law Gompertz (1825) by proposing a multi-factor exponential model. The proposed framework is based on the Laguerre approximating functions, and is able to capture flexible mortality patterns, and allows for a convenient estimation and prediction algorithm. An extensive empirical analysis is conducted using the proposed framework with a merged mortality database containing a large number of countries and regions with credible old-age mortality data. We find that the proposed exponential model leads to superior goodness-of-fit to historical data, and better out-of-sample forecast performance. Moreover, the exponential model predicts more balanced mortality improvements across ages, and thus leads to higher projected remaining life expectancy for the old ages than existing Gompertz-based mortality models. Finally, the modeling capacity of the proposed exponential model is further demonstrated by a multi-population extension, and an illustrative example of estimation and forecast is provided.

Keywords: Old Age Mortality Forecasting, Gompertz Law, Factor Model

JEL Classification: C0, J0

Suggested Citation

Li, Hong and Tan, Ken Seng and Tuljapurkar, Shripad and Zhu, Wenjun, Gompertz Law Revisited: Forecasting Mortality with a Multi-factor Exponential Model (December 31, 2019). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3495369 or http://dx.doi.org/10.2139/ssrn.3495369

Hong Li

Warren Centre for Actuarial Studies and Research, University of Manitoba ( email )

638 Drake Centre, 181 Freedman Crescent
Winnipeg, MB R3T 2N2
Canada

HOME PAGE: http://https://hongliecon.weebly.com/

Ken Seng Tan

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Shripad Tuljapurkar

Stanford University ( email )

Stanford, CA 94305
United States

Wenjun Zhu (Contact Author)

Nanyang Business School, Nanyang Technological University ( email )

50 Nanyang Avenue
Singapore, 639798
Singapore
(65) 6592-1859 (Phone)

HOME PAGE: http://sites.google.com/view/wenjun-zhu

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