Measuring the Longevity Tail of the Pension Gap: A Longevity-at-Risk Framework for Annuity, Pension, and Risk-Transfer Markets

<title>Abstract</title> <p>Rising longevity widens the pensions gap by increasing the duration and cost of retirement-income promises. This paper develops Longevity-at-Risk (LaR) as a backtestable, liability-linked measure of adverse mortality improvement. LaR is defined as the upper-tail quantile of mortality improvement for a given age, country, and forecast horizon. We extend the framework by introducing liability-based LaR, which translates adverse mortality-improvement scenarios into survival probabilities and annuity present-value stress, and Conditional Longevity-at-Risk, which measures tail risk conditional on cross-population longevity stress. Using data from the Human Mortality Database for eight developed economies, we estimate mortality-improvement distributions for ages 50–100 and horizons of 1, 5, 10, and 20 years. Composite Quantile LaR delivers lower coverage error and lower pinball loss than formal Lee–Carter and Cairns–Blake–Dowd benchmarks on the common seven-country sample. The framework provides a transparent tail-risk metric for annuity pricing, pension risk transfer, longevity reinsurance, solvency stress testing, and risk appetite governance.</p>