Forecasting mortality rates with a general stochastic mortality trend model

Abstract

This paper presents a model, which can closely estimate the future mortality rates whose efficiency is performed through the comparisons with respect to Lee-Carter and mortality trend models. This general model estimates the logit function of death rate in terms of general tendency of the mortality evolution independent of age, the mortality steepness, additional effects of childhood, youth and old age. Generalized linear model (GLM) is used to estimate the parameters. Moreover, the weighted least square (WLS) and random walk with drift (RWWD) methods are employed to project the future values of the parameters. In order to ensure the stability of the outputs and construct the confidence intervals, Monte Carlo simulation is used. The impact of the proposed model is implemented on USA, France, Italy, Japan and Israel mortality rates for both genders based on their ageing structure. A detailed comparison study is performed to illustrate modified mortality rates on the net single premiums over mortality trend model and Lee-Carter model.

Keywords

• Mortality trend model,Lee-Carter,GLM,Simulation,Random Walk,Weighted least squares

References

1. Börger, M., Deterministic shock vs. stochastic value-at-risk-an analysis of the Solvency II standard model approach to longevity risk, Blätter der DGVFM, 31(2) (2010), 225-259.
2. Börger, M., Fleischer, D. and Kuksin, N., Modeling the mortality trend under modern solvency regimes, Astin Bulletin, 44(01) (2014), 1-38.
3. Carter, L. and Lee, R.D., Modeling and Forecasting U.S. Mortality: Differentials in Life Expectancy by Sex., International Journal of Forecasting 8(3) (1992), 393-412.
4. Girosi, F and King, G.,. Understanding the Lee-Carter mortality forecasting method. Gking. Harvard. Edu., 2007.
5. Hasgul, E., Modeling Future Mortality Rates using Both Deterministic and Stochastic Approaches, unpublished M.Sc. Thesis, METU Institute of Applied Mathematics, 2015.
6. Heligman, L. and Pollard, J. H., The age pattern of mortality, Journal of the Institute of Actuaries, 107(01) (1980), 49-80.
7. Human Mortality Database, University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de (data downloaded on [12.07.16]).
8. Jarner, S. F. and Kryger, E. M., Modelling adult mortality in small populations: The SAINT model, Astin Bulletin, 41(02) (2011), 377-418.

9. Li, J. S. H. and Hardy, M. R., Measuring basis risk in longevity hedges, North American Actuarial Journal, 15(2) (2011), 177-200.
10. Li, N. and Lee, R., Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography, 42(3) (2005), 575-594.
11. Plat, R., One-year value-at-risk for longevity and mortality, Insurance: Mathematics and Economics, 49(3) (2011), 462-470.
12. Richards, S. J., Currie, I. D. and Ritchie, G. P., A value-at-risk framework for longevity trend risk, British Actuarial Journal, 19(01) (2014), 116-139.
13. Slud, E. V., Actuarial mathematics and life-table statistics, Chapman & Hall/CRC, 2012.
14. Sweeting, P. J., A trend-change extension of the Cairns-Blake-Dowd model, Annals of Actuarial Science, 5(2) (2011), 143-162.