A Gravity Model of Mortality Rates for Two Related Populations
City University London - Sir John Cass Business School
Andrew J. G. Cairns
Heriot-Watt University - Department of Actuarial Science & Statistics
David P. Blake
City University London - Cass Business School - The Pensions Institute
Pacific Global Advisors
December 1, 2011
North American Actuarial Journal, Vol. 15, No. 2, 2011
The mortality rate dynamics between two related but different-sized populations are modeled consistently using a new stochastic mortality model that we call the gravity model. The larger spreads (or deviations) relative to the evolution of the former, but the spreads in the period and cohort effects between the larger and smaller populations depend on gravity or spread reversion parameters for the two effects. The larger the two gravity parameters, the more strongly the smaller population’s mortality rates move in line with those of the larger population in the long run. This is important where it is believed that the mortality rates between related populations should not diverge over time on grounds of biological reasonableness. The model is illustrated using an extension of the Age-Period-Cohort model and mortality rate data for English and Welsh males representing a large population and the Continuous Mortality Investigation assured male lives representing a smaller related population.
Accepted Paper Series
Date posted: January 24, 2012
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