Paper: arXiv 2609.39569

Authors: Duy-Minh Dang, Yukan Perumal

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework for spouse-protected tontines, combining actuarial science with neural network optimization. It demonstrates strong empirical rigor through numerical experiments calibrated to real-world data and a cross-country comparison. The novelty lies in its unique approach to spouse protection within tontines and the application of NN for decumulation policies.

Research Flowchart

  flowchart TD
    A[Research Goal: Develop Spouse-Protected Tontine for Household Decumulation] --> B{Methodology: Contract Design & Optimization};
    B --> C{Inputs: Actuarial Fairness, Mortality Credits, Household Demographics};
    C --> D[Computational Process: Neural-Network Optimization for Decumulation Policy];
    D --> E[Outcomes: Quantified Spouse-Continuation Costs, Book-Level Diversification Benefits, Cross-Country Relevance];