Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?

Abstract

This paper is concerned with the mathematical problem of allocating longevity-linked fund payouts in a pool where participants differ in both wealth (contributions) and health (mortality), particularly when these groups are relatively small in size. In other words, we offer a modelling framework for distributing longevity-risk pools' income and benefits (or “tontine winnings”) when participants are heterogeneous. Similar to the nascent literature on decentralized risk sharing (DRS), there are several equally plausible arrangements for sharing benefits (a.k.a. “skinning the tontine cat”) among survivors. We argue that the selected rule may depend on the extent of social cohesion within the longevity risk pool, ranging from solidarity and altruism to pure individualism. And, if actuarial fairness is a concern, we suggest introducing an administrator – which differs from a guarantor – to make the tontine pool payouts collectively actuarial fair. Fairness is in the sense that the group of participants will on average receive the same benefits as they collectively invested; and we provide the mathematical framework to implement that suggestion. One thing is for certain: actuarial science cannot offer design uniqueness for longevity-contingent claims; only a consistent methodology.