Stochastic Mortality Model with Fractional L\'evy Dynamics

A substantial body of empirical evidence suggests that stochastic mortality models ignoring long range dependence tend to underestimate life expectancy, which may lead to profound implications for pension schemes and funding arrangements. This paper addresses the modelling of stochastic mortality via a mixture of a fractional L\'evy process and standard Brownian motion. Our stochastic mortality model exhibits nice analytical tractability in actuarial valuations and flexibility in the choice of underlying L\'evy specifications. The long range dependence feature embedded in our stochastic mortality model is well reflected in our empirical studies on the mortality shocks during World War II and COVID-19. For efficient numerical pricing of longevity derivatives, we construct an effective singular value decomposition approximation scheme to overcome the computational challenges arising from the non-Markovian nature of the fractional L\'evy process. Truncation errors in singular value decomposition approximation can be reduced by an effective residual correction scheme.