Longevity Risk and the Grim Reaper’s Toxic Tail: The Survivor Fan Charts

David Blake, Kevin Dowd and A.J.G Cairns

This paper uses survivor fan charts to illustrate the prospective density
functions of future male survival rates. The fan charts are based on a version
of the Cairns–Blake–Dowd model of male mortality that provides a good fit to
recent mortality data for England andWales. They indicate that although none of
us can escape the Grim Reaper, survivorship uncertainty is greatest for males
aged a little over 90, confirming that there exists a ‘toxic tail’ for those institutions,
such as annuity and pension providers, which are obliged to make payments to
them for as long as they live. We also find that taking account of uncertainty in
the parameters of the underlying mortality model leads to major increases in
estimates of the widths of the fan charts.c 2008 Elsevier B.V. All rights reserved.

Keywords: Cairns–Blake–Dowd model; Mortality; Fan charts; Longevity risk;
Survival rates; Toxic tail

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