in this way, a tontine annuity could operate in perpetuity.
design a tontine fund, a tontine annuity, and finally, a tontine
In this Section, we propose a tontine annuity that closely resembles a variable annuity.
In a tontine annuity, mortality-gain distributions would not be paid out immediately when other members die.
It turns out that a tontine annuity constructed in this way closely resembles an actuarially fair variable annuity (i.e., one without insurance agent commissions or insurance company reserves, risk-taking, and profits).
For example, Table 6 shows a sample monthly statement for a member of a tontine annuity who lives through the first month after turning age 65 and who had exactly $250,000 in his account at the end of the prior month.
Alternatively, a tontine annuity could be designed to make monthly tontine-annuity distributions that mimic an inflation-adjusted variable annuity.
In short, a tontine annuity could be designed to resemble an actuarially fair variable annuity or an actuarially fair inflation-adjusted variable annuity.
For example, if the tontine annuity in Table 6 had earned $1000 of investment interest in that month, the balance in the account at the end of the month would have been $1000 higher, and, consequently, the monthly tontine distribution would have been $8.52 higher--$2141.52 instead of the $2133, as shown in Table 6 ($2141.52 = $252,041.67/117.6939).
A similar pooling scheme is presented by Sabin (2010) known as Fair Tontine Annuity, or FTA, in which "fairness" is achieved by ensuring that pool members' expected benefits did not depend on the mortality experience of others in the pool.
J., 2010, Fair Tontine Annuity, SSRN Working Paper.