Assessing the Solvency Risk of Insurance Portfolios via a Continuous Time Cohort Model

The paper describes a model that evaluates the solvency of a portfolio of assets and liabilities of an insurer subject to longevity risk and financial risks. Liabilities are evaluated at fair-value. Interest-rate risk can affect both assets and liabilities. Longevity risk is described via a continuous-time cohort model. We evaluate the impact of different investment and hedging strategies on the characteristics of the funding ratio of run-off portfolios at different time horizons. Numerical simulations, calibrated to UK historical data, show that systematic longevity risk is particularly important in the long-run and needs to be hedged. We highlight that portfolio size, investment choices and solvency requirements are deeply interconnected. Natural hedging techniques can effectively reduce the required solvency buffer when interest-rate risk is perfectly hedged.