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A gravity model of mortality rates for two related populations

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  • Dowd, Kevin
  • Cairns, Andrew
  • Blake, David
  • Coughlan, Guy
  • Khalaf-Allah, Marwa

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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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 35738.

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Date of creation: 2011
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Handle: RePEc:pra:mprapa:35738

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Keywords: Gravity model; mortality rates; related populations;

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  1. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
  2. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
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Cited by:
  1. Andrew J.G. Cairns & Kevin Dowd & David Blake & Guy D. Coughlan, 2014. "Longevity hedge effectiveness: a decomposition," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 14(2), pages 217-235, February.
  2. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
  3. Blake, David & Courbage, Christophe & MacMinn, Richard & Sherris, Michael, 2011. "Longevity risks and capital markets: The 2010-2011 update," MPRA Paper 34279, University Library of Munich, Germany.
  4. French, Declan, 2014. "International mortality modelling—An economic perspective," Economics Letters, Elsevier, Elsevier, vol. 122(2), pages 182-186.
  5. Ahcan, Ales & Medved, Darko & Olivieri, Annamaria & Pitacco, Ermanno, 2014. "Forecasting mortality for small populations by mixing mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 12-27.
  6. Wong, Tat Wing & Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Time-consistent mean–variance hedging of longevity risk: Effect of cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 56-67.

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