Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-28T23:11:37.888Z Has data issue: false hasContentIssue false
  • English
  • Français

EQUITABLE RETIREMENT INCOME TONTINES: MIXING COHORTS WITHOUT DISCRIMINATING

Published online by Cambridge University Press:  09 June 2016

Moshe A. Milevsky  and
Thomas S. Salisbury
Moshe A. Milevsky*
Affiliation:
Schulich School of Business & the IFID Centre, York University, Toronto
Thomas S. Salisbury
Affiliation:
Department of Mathematics and Statistics, York University, Toronto E-Mail: salt@yorku.ca
*
E-Mail: milevsky@yorku.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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, Piggott et al. (2005) or Donnelly et al. (2014). In this paper, we generalize the natural retirement income tontine introduced by Milevsky and Salisbury (2015) 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.

Keywords

Life annuitieslongevity riskpension riskinsurance history
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 3 , September 2016 , pp. 571 - 604
Copyright
Copyright © Astin Bulletin 2016 

References

Ashraf, B. (2015) Optimal Design of Retirement Income Products, M.A. Survey paper. Dept. of Mathematics & Statistics, York University, Toronto.Google Scholar
Cannon, E. and Tonks, I. (2008) Annuity Markets. UK: Oxford University Press.Google Scholar
Compton, C. (1833) 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, Printed by J. Powell, Hand Court, London: Upper Thames Street.Google Scholar
Donnelly, C. (2015) Actuarial fairness and solidarity in pooled annuity funds. ASTIN Bulletin, 45 (1), 49–74.Google Scholar
Donnelly, C., Guillen, M. and Nielsen, J.P. (2013) Exchanging mortality for a cost. Insurance: Mathematics and Economics, 52 (1), 65–76.Google Scholar
Donnelly, C., Guillén, M. and Nielsen, J.P. (2014) Bringing cost transparency to the life annuity market. Insurance: Mathematics and Economics, 56 (1), 14–27.Google Scholar
Doob, J.L. (1984) Classical Potential Theory and its Probabilistic Counterpart. New York: Springer Verlag.CrossRefGoogle Scholar
Hanewald, K., Piggott, J. and Sherris, M. (2013) Individual post-retirement longevity risk management under systematic mortality risk. Insurance: Mathematics and Economics, 52 (1), 87–97.Google Scholar
Milevsky, M.A. (2015) King William's Tontine: Why the Retirement Annuity of the Future Should Resemble Its Past. New York: Cambridge University Press.Google Scholar
Milevsky, M.A. and Salisbury, T.S. (2015) Optimal retirement income tontines. Insurance: Mathematics and Economics, 64 (1), 91–105 Google Scholar
Piggott, J., Valdez, E.A. and Detzel, B. (2005) The simple analytics of a pooled annuity fund. The Journal of Risk and Insurance, 72 (3), 497–520.Google Scholar
Qiao, C. and Sherris, M. (2013) Managing systematic mortality risk with group self-pooling and annuitization schemes. Journal of Risk and Insurance, 80 (4), 949–974.CrossRefGoogle Scholar
Sabin, M.J. (2010) Fair tontine annuity. Available at SSRN: http://ssrn.com/abstract=1579932 or http://dx.doi.org/10.2139/ssrn.1579932.CrossRefGoogle Scholar
Stamos, M.Z. (2008) Optimal consumption and portfolio choice for pooled annuity funds. Insurance: Mathematics and Economics, 43 (1), 56–68.Google Scholar
Tonti, L. (1654) Edict of the King for the Creation of the Society of the Royal Tontine, (ed. Haberman, S. and Sibbett, T.A.), Volume V. Translated by V. Gasseau-Dryer, History of Actuarial Science. London: William Pickering, 1995.Google Scholar
Valdez, E.A., Piggott, J. and Wang, L. (2006) Demand and adverse selection in a pooled annuity fund. Insurance: Mathematics and Economics, 39 (2), 251–266.Google Scholar
Yaari, M. (1965) Uncertain lifetime, life insurance and the theory of the consumer. Review of Economic Studies, 32 (2), 137–150.Google Scholar