Robust Mean-Variance Hedging of Longevity Risk

Parameter uncertainty and model misspecification can have a significant impact on the performance of hedging strategies for longevity risk. To mitigate this lack of robustness, we propose an approach in which the optimal hedge is determined by optimizing the worst-case value of the objective function with respect to a set of plausible probability distributions. In the empirical analysis, we consider an insurer who hedges longevity risk using a longevity bond, and we compare the worst-case (robust) optimal hedges with the classical optimal hedges in which parameter uncertainty and model misspecification are ignored. We find that unless the risk premium on the bond is close to zero, the robust optimal hedge is significantly less sensitive to variations in the underlying probability distribution. Moreover, the robust optimal hedge on average outperforms the nominal optimal hedge unless the probability distribution used by the nominal hedger is close to the true distribution.