Volterra mortality model: Actuarial valuation and risk management with long-range dependence

Abstract

While abundant empirical studies support the long-range dependence (LRD) of mortality rates, the corresponding impact on mortality securities is largely unknown due to the lack of appropriate tractable models for valuation and risk management purposes. We propose a novel class of Volterra mortality models that incorporate LRD into the actuarial valuation, retain tractability, and are consistent with the existing continuous-time affine mortality models. We derive the survival probability in closed-form solution by taking into account of the historical health records. The flexibility and tractability of the models make them useful in valuing mortality-related products such as death benefits, annuities, longevity bonds, and many others, as well as offering optimal mean–variance mortality hedging rules. Numerical studies are conducted to examine the effect of incorporating LRD into mortality rates on various insurance products and hedging efficiency.