Can an actuarially unfair tontine be optimal?

A one-period tontine is a collective investment fund in which every participant enters with an initial contribution, but only those participants who are still alive at maturity are entitled to receive a share of the total fund value. A vast literature proposes various sharing rules, primarily using actuarial fairness of the payout as the main criterion, i.e., the sharing is structured in a way that participants have the same (unconditional) expected return. We revisit this point and suggest alternative sharing rules aimed at better suiting investors. Specifically, we discuss how to share mortality risk using equality in expected utility among participants as our fairness criterion. A key finding is that, in a competitive market, only actuarially fair tontines are viable.