zbMATH — the first resource for mathematics

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.

91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography
Full Text: DOI
[1] Ashraf, B., (2015)
[2] Cannon, E.; Tonks, I., Annuity Markets, (2008), UK: Oxford University Press, UK
[3] Compton, C., A Treatise on Tontine: In Which The Evils of the Old System Are Exhibited and an Equitable Plan Suggested for Rendering the Valuable Principle of Tontine More Beneficially Applicable to Life Annuities, (1833), London: Upper Thames Street, London
[4] Donnelly, C., Actuarial fairness and solidarity in pooled annuity funds, ASTIN Bulletin, 45, 49-74, (2015) · Zbl 1390.91177
[5] Donnelly, C.; Guillen, M.; Nielsen, J. P., Exchanging mortality for a cost, Insurance: Mathematics and Economics, 52, 65-76, (2013) · Zbl 1291.91103
[6] Donnelly, C.; GuillĂ©n, M.; Nielsen, J. P., Bringing cost transparency to the life annuity market, Insurance: Mathematics and Economics, 56, 14-27, (2014) · Zbl 1304.91101
[7] Doob, J. L., Classical Potential Theory and its Probabilistic Counterpart, (1984), New York: Springer Verlag, New York · Zbl 0549.31001
[8] Hanewald, K.; Piggott, J.; Sherris, M., Individual post-retirement longevity risk management under systematic mortality risk, Insurance: Mathematics and Economics, 52, 87-97, (2013) · Zbl 1291.91113
[9] Milevsky, M. A., King William’s Tontine: Why the Retirement Annuity of the Future Should Resemble Its Past, (2015), New York: Cambridge University Press, New York
[10] Milevsky, M. A.; Salisbury, T. S., Optimal retirement income tontines, Insurance: Mathematics and Economics, 64, 91-105, (2015) · Zbl 1348.91176
[11] Piggott, J.; Valdez, E. A.; Detzel, B., The simple analytics of a pooled annuity fund, The Journal of Risk and Insurance, 72, 497-520, (2005)
[12] Qiao, C.; Sherris, M., Managing systematic mortality risk with group self-pooling and annuitization schemes, Journal of Risk and Insurance, 80, 949-974, (2013)
[13] Sabin, M. J., (2010)
[14] Stamos, M. Z., Optimal consumption and portfolio choice for pooled annuity funds, Insurance: Mathematics and Economics, 43, 56-68, (2008) · Zbl 1140.91411
[15] Tonti, L.; Haberman, S.; Sibbett, T. A., Edict of the King for the Creation of the Society of the Royal Tontine, (1654), London: William Pickering, London
[16] Valdez, E. A.; Piggott, J.; Wang, L., Demand and adverse selection in a pooled annuity fund, Insurance: Mathematics and Economics, 39, 251-266, (2006) · Zbl 1098.91078
[17] Yaari, M., Uncertain lifetime, life insurance and the theory of the consumer, Review of Economic Studies, 32, 137-150, (1965)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.