Neural-Network Optimization of Spouse-Protected Tontine Decumulation

Summary

This paper designs a spouse-protected tontine for household retirement income. A first death changes the household’s status without triggering a transfer from the pool; the account stays with the contract and can fund a spouse-only continuation if the retiree dies first. The authors derive actuarial-fairness conditions and a mortality-credit allocation rule that balances exactly after outcomes are realized. For a representative household, they formulate withdrawal and rebalancing decisions to maximize expected cumulative real payments while accounting for the Conditional Value-at-Risk of terminal shortfalls against reserve targets, without requiring survival to the horizon.

A global-in-time neural-network policy parameterization provides the numerical solution. Experiments calibrated to Australia find spouse continuation to be a substantial, persistent household event. In the large-book limit, diversification removes most of the representative-contract excess upper-tail continuation cost, while expected cost per contract is unchanged. A cross-country mortality comparison suggests the pattern is not unique to Australia. These are modeled numerical findings; the supplied text does not give calibration details or establish outcomes for actual tontine products.

Key ideas

• The contract keeps the account attached to the household after the first death and can support a spouse-only continuation phase.
• The proposed mortality-credit allocation rule achieves exact ex post budget balance.
• Household withdrawals and rebalancing are optimized against expected payments and CVaR of terminal reserve shortfalls.
• Neural networks parameterize admissible control policies over the full time horizon.
• In the reported large-book limit, diversification reduces much of the excess upper-tail continuation cost without changing expected cost per contract.

Tags

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


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









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.

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