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Multi-period extension of the tontine fund framework

Develop a multi-period tontine fund model by constructing a sequence of linked one-period funds and define the explicit dynamic relations between consecutive periods’ survival indicator vectors It, investment (premium) vectors πt, share allocation vectors ft, and payout vectors Wt.

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Background

The paper focuses on a single-period tontine fund and its fairness, payout, and share allocation structures. Extending to multiple periods requires specifying how the model’s core components evolve and link across time.

The authors explicitly identify the need to define the dynamic relationships among indicator, premium, share, and payout vectors across consecutive periods, leaving this for future research.

References

The next step is to extend this one-period framework to a multiperiod tontine fund, which would be constructed as a sequence of linked one-period funds. Defining the relations between indicator vectors, premium vectors, share allocation vectors, and the all-important payout vectors in consecutive periods is left in an honoured tradition for future research.

— 'Egalitarian pooling and sharing of longevity risk', a.k.a. 'The many ways to skin a tontine cat' (2402.00855 - Dhaene et al., 1 Feb 2024) in Section 7 (Summary and Conclusion)