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

2026-02-18

AI Summary

This study addresses how retirees can optimally manage withdrawal and asset allocation decisions under longevity risk and bequest motives to balance lifetime income against tail risk in terminal wealth. To this end, the authors develop a personal tontine account model with a refund guarantee and, for the first time, apply neural network methods to solve this high-dimensional dynamic control problem. The framework incorporates international asset allocation, stochastic mortality, and Conditional Value-at-Risk (CVaR) as a risk measure, enabling actuarially sound pricing through simulation. The findings reveal that combining international diversification with longevity risk pooling significantly improves the trade-off between expected withdrawals and tail risk. The optimal strategy employs foreign equities as a state-dependent catch-up instrument, and the cost of the refund guarantee is primarily driven by extreme tail scenarios.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Fair Division
• Machine Learning: Life-Long and Continual Learning

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Economics, Online Markets and Human Computation: The sharing economy
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications

Abstract

Money-back guarantees (MBGs) are features of pooled retirement income products that address bequest concerns by ensuring the initial premium is returned through lifetime payments or, upon early death, as a death benefit to the estate. This paper studies optimal retirement decumulation in an individual tontine account with an MBG overlay under international diversification and systematic longevity risk. The retiree chooses withdrawals and asset allocation dynamically to trade off expected total withdrawals (EW) against the Conditional Value-at-Risk (CVaR) of terminal wealth, subject to realistic investment constraints. The optimization is solved under a plan-to-live convention, while stochastic mortality affects outcomes through its impact on mortality credits at the pool level. We develop a neural-network based computational approach for the resulting high-dimensional, constrained control problem. The MBG is priced ex post under the induced EW--CVaR optimal policy via a simulation-based actuarial rule that combines expected guarantee costs with a prudential tail buffer. Using long-horizon historical return data expressed in real domestic-currency terms, we find that international diversification and longevity pooling jointly deliver the largest improvements in the EW--CVaR trade-off, while stochastic mortality shifts the frontier modestly in the expected direction. The optimal controls use foreign equity primarily as a state-dependent catch-up instrument, and implied MBG loads are driven mainly by tail outcomes (and the chosen prudential buffer) rather than by mean payouts.

Problem

• retirement decumulation
• money-back guarantee
• systematic longevity risk
• international diversification
• tontine

Innovation

• neural-network optimization
• money-back tontine
• systematic longevity risk
• international diversification
• CVaR-EW trade-off