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European Actuarial Journal

, Volume 6, Issue 1, pp 61–96 | Cite as

A credibility approach of the Makeham mortality law

  • Yahia Salhi
  • Pierre-E. Thérond
  • Julien Tomas
Original Research Paper

Abstract

Interest from life insurers to assess their portfolios’ mortality risk has considerably increased. The new regulation and norms, Solvency II, shed light on the need of life tables that best reflect the experience of insured portfolios in order to quantify reliably the underlying mortality risk. In this context and following the work of Bühlmann and Gisler (A course in credibility theory and its applications. Springer, New York, 2005) and Hardy and Panjer (ASTIN Bull 28(2):269–283, 1998), we propose a credibility approach which consists on reviewing, as new observations arrive, the assumption on the mortality curve. Unlike the methodology considered in Hardy and Panjer (1998) that consists on updating the aggregate deaths we have chosen to add an age structure on these deaths. Formally, we use a Makeham graduation model. Such an adjustment allows to add a structure in the mortality pattern which is useful when portfolios are of limited size so as to ensure a good representation over the entire age bands considered. We investigate the divergences in the mortality forecasts generated by the classical credibility approaches of mortality including Hardy and Panjer (1998) and the Poisson-Gamma model on portfolios originating from various French insurance companies.

Keywords

Credibility Makeham law Mortality Life insurance Graduation Extrapolation 

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Copyright information

© DAV / DGVFM 2016

Authors and Affiliations

  • Yahia Salhi
    • 1
  • Pierre-E. Thérond
    • 1
    • 2
  • Julien Tomas
    • 3
  1. 1.Univ Lyon, Université Lyon 1, LSAFLyonFrance
  2. 2.Galea & AssociésParisFrance
  3. 3.SCOR Global LifeParis Cedex 16France

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