Optimal retirement products under subjective mortality beliefs

Many empirical studies confirm that policyholder's subjective mortality beliefs deviate from the information given by publicly available mortality tables. In this study, we look at the effect of subjective mortality beliefs on the perceived attractiveness of retirement products, focusing on two extreme products, conventional annuities (where the insurance company takes the longevity risk) and tontines (where a pool of policyholders shares the longevity risk). If risk loadings and charges are neglected, a standard expected utility framework, without subjective mortality beliefs, leads to the conclusion that annuities are always preferred to tontines (Yaari (1965), Milevsky and Salisbury (2015)). In the same setting, we show that this result is easily reversed if an individual perceives her peer's life expectancies to be lower than the ones used by the insurance company. We prove that, assuming such subjective beliefs, there exists a critical tontine pool size from which the tontine is always preferred over the annuity. This suggests that tontines might be perceived as much more attractive than suggested by standard expected utility theory without subjective mortality beliefs.