Money-Back Tontines for Retirement Decumulation: Neural-Network Optimization under Systematic Longevity Risk

German Nova Orozco, Duy-Minh Dang and Peter A. Forsyth

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Abstract: Money-back guarantees (MBGs) address bequest concerns in pooled retirement income products by returning the initial purchase price through withdrawals or, after early death, through a benefit to the member's beneficiaries or estate. We study the distinct actuarial problem created by adding an MBG to an individual-account tontine with dynamic withdrawals, investment in domestic and foreign assets, and systematic longevity risk. The retiree trades expected withdrawals (EW) against the lower-tail Conditional Value-at-Risk (CVaR) of terminal wealth under a fixed-horizon plan-to-live convention. Neural networks parameterize admissible withdrawal and rebalancing controls; the MBG is then valued ex post under the learned policy through an equivalent up-front load combining the expected payout with an upper-tail CVaR prudential buffer. We also approximate the effect of contract pooling on per-contract tail risk and pricing. Using long-horizon market and mortality data calibrated for an Australian retiree, we find that expected MBG payouts are modest, while the representative-contract payout has a severe upper tail. Contract pooling substantially reduces the upper-tail exposure on a per-contract basis and lowers the approximate pooled-contract load. International diversification materially improves the EW--CVaR retirement-income trade-off, while affecting the MBG payout distribution and equivalent load only modestly. Stochastic mortality likewise has a modest effect on the efficient frontier and MBG pricing.

Date: 2026-02, Revised 2026-09
New Economics Papers: this item is included in nep-age, nep-cmp and nep-rmg
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