Facing Up to Longevity with Old Actuarial Methods: A Comparison of Pooled Funds and Income Tontines

We compare the concepts underlying modern actuarial solutions to pension insurance and present two recently developed pension products—pooled annuity overlay funds (based on actuarial fairness) and equitable income tontines (based on equitability). These two products adopt specific approaches to the management of longevity risk by mutualising it among participants rather than transferring it completely to the insurer. As the market would appear to be ready for such innovations, our study seeks to establish a general framework for their introduction. We stress that the notion of actuarial fairness, which characterises pooled annuity overlay funds, enables participants to join and exit the fund at any time. Such freedom of action is a quite remarkable feature and one that cannot be matched by lifelong contracts

Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits

This paper studies the distribution of particular weighted sums of Bernoulli random variables. The computing methods are applied to derive the probability distribution of the random amount of survivor credits to be shared among surviving participants in singleperiod tontine schemes. The effectiveness of this new arrangement can then be evaluated beyond the classical analysis based on crude approximations for the two first moments, only