Optimal retirement income tontines

Tontines were once a popular type of mortality-linked investment pool. They promised enormous rewards to the last survivors at the expense of those died early. While this design appealed to the gambling instinct, it is a suboptimal way to generate retirement income. Indeed, actuarially-fair life annuities making constant payments–where the insurance company is exposed to longevity risk–induce greater lifetime utility. However, tontines do not have to be structured the historical way, i.e. with a constant cash flow shared amongst a shrinking group of survivors. Moreover, insurance companies do not sell actuarially-fair life annuities, in part due to aggregate longevity risk.