Spouse-Protected Tontines: Household Decumulation via Neural-Network Optimization

2026-09-30

AI Summary

This study addresses the challenges of abrupt household state transitions and subsequent fund allocation arising from the death of one spouse in reversionary annuities. To tackle this, it constructs an actuarially fair model incorporating a “no-transfer first-death” mechanism and proposes a neural network-based global time-control parameterization approach. By integrating Conditional Value-at-Risk (CVaR) with large-pool approximation techniques, the method effectively solves the multidimensional stochastic decumulation control problem. Empirical validation using Australian data demonstrates that portfolio diversification significantly mitigates tail costs, confirms the universality of the surviving-spouse phase, and achieves an effective balance between payout adequacy and risk management.

Abstract

We develop a spouse-protected tontine in which a first death changes the household state but generates no pool transfer. The same account remains attached to the household contract until extinction and funds a spouse-only continuation phase if the retiree dies first. We derive contract-level actuarial-fairness conditions and a finite-pool mortality-credit allocation rule with exact ex post budget balance. Under a homogeneous large-pool approximation, we formulate a multidimensional decumulation problem for a representative household, with withdrawal and rebalancing controls while the retiree is alive. The objective balances expected cumulative real household payments against the Conditional Value-at-Risk (CVaR) of terminal shortfalls relative to household reserve targets, without conditioning on survival to the horizon. We develop a numerical solution method for this problem based on a global-in-time neural-network parameterization of admissible control policies. We quantify policy-induced spouse-continuation costs using expected-cost and risk-loaded payment-scale loads at both representative-contract and book levels. We characterize the large-book limit of average per-contract continuation cost as the expected representative-contract cost conditional on common market information. Numerical experiments calibrated to Australia show that the spouse-only phase is a first-order and persistent household event. In these experiments, book-level diversification removes most of the representative-contract excess upper-tail cost of spouse continuation in the large-book limit, without changing expected per-contract continuation cost. A cross-country mortality comparison indicates that the prevalence and persistence of the spouse-only phase are not specific to Australia.

Problem

• Tontine
• Household decumulation
• Spouse protection
• Retirement income
• Risk management

Innovation

• Spouse-Protected Tontines
• Neural-Network Optimization
• Conditional Value-at-Risk (CVaR)
• Household Decumulation
• Mortality-Credit Allocation