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

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.