This paper investigates whether annuities and tontines can be combined in a retirement portfolio. It borrows from Tobin's two-fund separation and uses the mean-variance efficient frontier as a framework. Analytical and numerical results show that standard tontine designs, especially the natural tontine, are highly correlated with annuities, which limits diversification and often leads to corner solutions with full allocation to one of the two products. To overcome this, the paper introduces the power tontine as a flexible tool with a tunable payout function. A simple calibration rule is proposed to identify tontine payout profiles that improve the mean-variance trade-off and support balanced annuity-tontine allocations. The study connects actuarial product design with portfolio theory, and illustrates how investment principles can guide retirement income innovation.
We study a retiree's optimal consumption, portfolio choice, and irreversible annuitization over a random lifetime. We use Cobb-Douglas preferences over consumption and annuity income to capture a tradeoff between longevity insurance and liquidity, and we allow annuity income to serve as collateral for borrowing. The optimal policy has a transparent threshold structure driven by the wealth-to-annuity ratio. Annuity purchases occur only when this ratio reaches an endogenous upper trigger, while consumption and portfolio rules adjust smoothly in the interior. The collateral constraint generates endogenous de-risking: the optimal risky position is reduced as the retiree approaches the solvency limit and vanishes at the boundary. Numerical comparative statics show that a stronger preference for liquid consumption delays annuitization and increases risk-taking per unit of annuity income, whereas a more generous credit line lowers the effective illiquidity cost of annuities and induces earlier annuitization. These results provide economically and actuarially interpretable predictions on how annuitization preferences and borrowing capacity jointly shape leverage, risk exposure, and the timing of annuity purchases.
This paper studies optimal investment and benefit payment strategies for a target benefit pension plan under loss aversion. The plan manager maximizes discounted S-shaped utility from benefit payments, subject to a downside constraint. The target benefit is determined by an actuarial equivalence condition linking contributions and benefits, while deviations from the target reflect intergenerational risk sharing. The pension fund invests in a risk-free asset and multiple risky assets. Using the martingale approach, we derive explicit solutions for the optimal investment and benefit payment strategies. Numerical illustrations and sensitivity analyzes highlight the effects of key market parameters on the optimal policies.
