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Equitable retirement income tontines: mixing cohorts without discriminating. (English) Zbl 1390.91201
Summary: There is growing interest in the design of pension annuities that insure against idiosyncratic longevity risk while pooling and sharing systematic risk. This is partially motivated by the desire to reduce capital and reserve requirements while retaining the value of mortality credits; see for example, [J. Piggott et al., “The simple analytics of a pooled annuity fund”, J. Risk Insur. 72, No. 3, 497–520 (2005; doi:10.1111/j.1539-6975.2005.00134.x); C. Donnelly et al., Insur. Math. Econ. 56, 14–27 (2014; Zbl 1304.91101)]. In this paper, we generalize the natural retirement income tontine introduced by the authors [Insur. Math. Econ. 64, 91–105 (2015; Zbl 1348.91176)] by combining heterogeneous cohorts into one pool. We engineer this scheme by allocating tontine shares at either a premium or a discount to par based on both the age of the investor and the amount they invest. For example, a 55-year old allocating $10,000 to the tontine might be told to pay $200 per share and receive 50 shares, while a 75-year old allocating $8,000 might pay $40 per share and receive 200 shares. They would all be mixed together into the same tontine pool and each tontine share would have equal income rights. The current paper addresses existence and uniqueness issues and discusses the conditions under which this scheme can be constructed equitably – which is distinct from fairly – even though it isn’t optimal for any cohort. As such, this also gives us the opportunity to compare and contrast various pooling schemes that have been proposed in the literature and to differentiate between arrangements that are socially equitable, vs. actuarially fair vs. economically optimal.

MSC:
91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography
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