A Gravity Model of Mortality Rates for Two Related Populations |
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| Authors: | Kevin Dowd PhD Andrew J. G. Cairns PhD David Blake PhD Guy D. Coughlan PhD Marwa Khalaf-Allah PhD |
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| Affiliation: | 1. Pensions Institute, Cass Business School , 106 Bunhill Row, London, EC1Y 8TZ , United Kingdom;2. Financial Mathematics at the Maxwell Institute for Mathematical Sciences, and Actuarial Mathematics and Statistics , Heriot-Watt University , Edinburgh, EH14 4AS , United Kingdom;3. Pension Economics and Director of the Pensions Institute at the Director of the Pensions Institute at the Pensions Institute , Cass Business School , 106 Bunhill Row, London, EC1Y 8TZ , United Kingdom;4. Pension Advisory Group , J.P. Morgan, 125 London Wall, London, EC2Y 5AJ , United Kingdom |
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| Abstract: | Abstract 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 population is modeled independently, and the smaller population is modeled in terms of 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. |
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