Market-Consistent Valuation and Capital Assessment for Demographic Risk in Life Insurance: A Cohort Approach

We explore the quantification of demographic risk in accordance with the market-consistent actuarial valuation principles. Our contribution includes closed formulas for assessing the inflows and outflows of an insurance policy portfolio using a cohort approach. To maintain versatility, we address both traditional and equity-linked policies, providing a market-consistent valuation of liabilities. Subsequently, we compute the capital requirement for idiosyncratic risk (linked to accidental mortality) and systematic risk (trend risk), presenting an approach that allows consideration of the risks at cohort level. Specifically, we evaluate the minimum capital using an annual time horizon, a 99.5% confidence level, and the Value at Risk as the risk measure, developing a framework aligned with the European Solvency II regulation for insurance and reinsurance companies. Moreover, the model can be easily adapted to accommodate other regulatory frameworks, incorporating specific rules and accounting principles relevant to diverse jurisdictions worldwide. The numerical analysis and the sensitivities reveal that the accidental volatility of policyholders’ deaths is influenced by the inherent characteristics of the cohort’s policies, the age of policyholders, and the variability of sums insured. Furthermore, trend risk is contingent on both accidental volatility and the longevity forecasting model employed.