Actuarial Fairness and Solidarity in Pooled Annuity Funds

Abstract

Various types of structures that enable a group of individuals to pool their mortality risk have been proposed in the literature. Collectively, the structures are called pooled annuity funds. Since the pooled annuity funds propose different methods of pooling mortality risk, we investigate the connections between them and find that they are genuinely different for a finite heterogeneous membership profile.We discuss the importance of actuarial fairness, defined as the expected benefits equalling the contributions for each member, in the context of pooling mortality risk and comment on whether actuarial unfairness can be seen as solidarity between members. We show that, with a finite number of members in the fund, the group self-annuitization scheme is not actuarially fair: some members subsidize the other members. The implication is that the members who are subsidizing the others may obtain a higher expected benefit by joining a fund with a more favourable membership profile. However, we find that the subsidies are financially significant only for very small or highly heterogeneous membership profiles.

Optimal retirement income tontines

“…It is not widely known that in the year 1790, the first U. Tontines not only have a fascinating history but have some basis in economic principles, In fact, Adam Smith himself, writing in the Wealth of Nations, noted that tontines may be 14 Source: Jennings, Swanson and Trout (1988). 15 Hamilton left public life in disgrace after admitting to an affair with a married woman, and soon after died in a duel with Aaron Burr, the U.S. vice president at the time 16 Source: Ransom and Sutch (1987).…”

“…where ξ lies between (1 − η)µ and (1 + η)µ. Applying (14), (15), and (16) yields a constant C 2 such that if n ≥ n 1 and 1 ≥ p ≥ p 1 then…”

Comparison of the costs of the defined-benefit and the defined-contribution schemes under an actuarial methodology

“…There are arguments in favor and against conceiving intergenerational solidarity as a com-ponent of the so-called actuarial fairness principle (see (Bräutigam, Guillen, y Nielsen, 2017;Donnelly, 2015;Landes, 2015;Meneu, Devesa, Devesa, Domínguez, y Encinas, 2016)). This notion states that individuals should pay premia that reflect the risks they bring to the collectivity, and of course serves to establish a fair and adequate price for a given risk.…”

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

“…A lump sum payment gave the right to an annuity and this lifelong pension increased over time, as the yields were increasingly distributed among a smaller number of surviving beneficiaries. Likewise, modern tontine-type annuity products reduce longevity risk for the companies providing them, and they can therefore be offered to customers at a lower cost (see, Donnelly 2015).…”