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Historical tontines promised enormous rewards to the last survivors at theexpense of those who died early. While this design appealed to the gamblinginstinct, it is a suboptimal way to manage longevity risk during retirement.This is why fair life annuities making constant payments -- where the insurancecompany is exposed to the longevity risk -- induces greater lifetime utility.However, tontines do not have to be designed using a winner-take-all approachand insurance companies do not actually sell fair life annuities, partially dueto aggregate longevity risk.  In this paper we derive the tontine structure that maximizes lifetimeutility, but doesn't expose the sponsor to any longevity risk. We examine itssensitivity to the size of the tontine pool; individual longevity riskaversion; and subjective health status. The optimal tontine varies with theindividual's longevity risk aversion $\gamma$ and the number of participants$n$, which is problematic for product design. That said, we introduce astructure called a natural tontine whose payout declines in exact proportion tothe (expected) survival probabilities, which is near-optimal for all $\gamma$and $n$. We compare the utility of optimal tontines to the utility of loadedlife annuities under reasonable demographic and economic conditions and findthat the life annuity's advantage over tontines, is minimal.  We also review and analyze the first-ever mortality-derivative issued by theBritish government, known as King Williams's tontine of 1693. We shed light onthe preferences and beliefs of those who invested in the tontines vs. theannuities and argue that tontines should be re-introduced and allowed toco-exist with life annuities. Individuals would likely select a portfolio oftontines and annuities that suit their personal preferences for consumption andlongevity risk, as they did over 320 years ago.

Optimal Retirement Tontines for the 21st Century: With Reference to Mortality Derivatives in 1693