Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T16:49:40.306Z Has data issue: false hasContentIssue false
  • English
  • Français

TONUITY: A NOVEL INDIVIDUAL-ORIENTED RETIREMENT PLAN

Published online by Cambridge University Press:  26 December 2018

An Chen ,
Peter Hieber  and
Jakob K. Klein
An Chen
Affiliation:
Institute of Insurance ScienceUniversity of Ulm, Ulm, Germany E-Mail: [email protected]
Peter Hieber
Affiliation:
Institute of Insurance ScienceUniversity of Ulm, Ulm, Germany E-Mail: [email protected]
Jakob K. Klein*
Affiliation:
Institute of Insurance ScienceUniversity of Ulm, Ulm, Germany E-Mail: [email protected]
*
E-Mail: [email protected]
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.

For insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (e.g., conventional annuities). Insurance companies might react by price increases for those products, and, at the same time, might think of alternatives that shift longevity risk (at least partially) to policyholders. In the extreme case, this leads to so-called tontine products where the insurance company’s role is merely administrative and longevity risk is shared within a pool of policyholders. From the policyholder’s viewpoint, such products are, however, not desirable as they lead to a high uncertainty of retirement income at old ages. In this article, we alternatively suggest a so-called tonuity that combines the appealing features of tontine and conventional annuity. Until some fixed age (the switching time), a tonuity’s payoff is tontine-like, afterwards the policyholder receives a secure payment of a (deferred) annuity. A tonuity is attractive for both the retiree (who benefits from a secure income at old ages) and the insurance company (whose capital requirements are reduced compared to conventional annuities). The tonuity is a possibility to offer tailor-made retirement products: using risk capital charges linked to Solvency II, we show that retirees with very low or very high risk aversion prefer a tontine or conventional annuity, respectively. Retirees with medium risk aversion, however, prefer a tonuity. In a utility-based framework, we therefore determine the optimal tonuity characterized by the critical switching time that maximizes the policyholder’s lifetime utility.

Keywords

Longevity risktontinesSolvency IIpooled annuitiescapital requirementslifetime utility
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 5 - 30
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Astin Bulletin 2018

References

Bauer, D., Börger, M. and Russ, J. (2010) On the pricing of longevity-linked securities. Insurance: Mathematics & Economics, 46(1), 139–149.Google Scholar
Börger, M. (2010) Deterministic shock vs. stochastic Value-at-Risk– an analysis of the Solvency II standard model approach to longevity risk. Blätter der DGVFM, 31, 225–259.CrossRefGoogle Scholar
Directive 2009/138/EC. (2009) Directive 2009/138/EC of the European Parliament and of the Council on the taking-up and pursuit of the business of insurance and reinsurance (Solvency II). Technical Report, European Parliament and the Council.Google Scholar
Donnelly, C. (2015) Actuarial fairness and solidarity in pooled annuity funds. ASTIN Bulletin, 45(1), 49–74.CrossRefGoogle Scholar
Donnelly, C., Guillén, M. and Nielsen, J.P. (2013) Exchanging uncertain mortality for a cost. Insurance: Mathematics and Economics, 52, 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, 14–27.Google Scholar
EIOPA. (2014) Technical specifications for the Solvency II preparatory phase - Part I. Technical Report, EIOPA.Google Scholar
Fries, J.F. (1980) Aging, natural death, and the compression of morbidity. The New England Journal of Medicine, 303 (3), 130–135.CrossRefGoogle ScholarPubMed
Gelfand, I. and Fomin, S. (1963) Calculus of Variations. Revised English edition translated (ed. Silverman, R.A.). Englewood Cliffs, NJ: Prentice-Hall Inc.Google Scholar
Gompertz, B. (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513–583.Google Scholar
Gründl, H. and Weinert, J.-H. (2016) The modern tontine: An innovative instrument for longevity provision in an ageing society. ICIR Working Paper Series No. 22/2016. URL: http://www.icir.de/fileadmin/user_upload/WP_22_17.pdf.Google Scholar
Gumbel, E. (1958) Statistics of Extremes, p. 247. New York: Columbia Univ. press.CrossRefGoogle Scholar
Huang, H.X. and Milevsky, M.A. (2011) Spending retirement on planet vulcan: The impact of longevity risk aversion on optimal withdrawal rates. Financial Analyst Journal, 67(2), 45–58.Google Scholar
Knoblauch, A. (2008) Closed-form expressions for the moments of the binomial probability distribution. SIAM Journal on Applied Mathematics, 69(1), 197–204.CrossRefGoogle Scholar
Lin, Y. and Cox, S. (2005) Securitization of mortality risks in life annuities. Journal of Risk and Insurance, 72(2), 227–252.CrossRefGoogle Scholar
Menoncin, F. (2008) The role of longevity bonds in optimal portfolios. Insurance: Mathematics and Economics, 42(1), 343–358.Google Scholar
Milevsky, M. and Salisbury, T. (2015) Optimal retirement income tontines. Insurance: Mathematics & Economics, 64, 91–105.Google Scholar
Milevsky, M.A. and Salisbury, T.S. (2016) Equitable retirement income tontines: Mixing cohorts without discriminating. ASTIN Bulletin, 46(3), 571–604.CrossRefGoogle Scholar
Olivieri, A. and Pitacco, E. (2009) Stochastic mortality: The impact on target capital. Astin Bulletin, 39(02), 541–563.CrossRefGoogle Scholar
Piggott, J., Valdez, E.A. and Detzel, B. (2005) The simple analytics of a pooled annuity fund. Journal of Risk and Insurance, 72(3), 497–520.CrossRefGoogle Scholar
Pitacco, E., Denuit, M., Haberman, S. and Olivieri, A. (2009) Modelling Longevity Dynamics for Pensions and Annuity Business. Oxford: Oxford University Press.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
Ransom, R.L. and Sutch, R. (1987) Tontine insurance and the Armstrong investigation: A case of stifled innovation, 1868–1905. Journal of Economic History, 47(2), 379–90.CrossRefGoogle Scholar
Richards, S. (2012) A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal, 2012(4), 233–257.CrossRefGoogle Scholar
Richter, A. and Weber, F. (2011) Mortality-indexed annuities managing longevity risk via product design. North American Actuarial Journal, 15(2), 212–236.CrossRefGoogle Scholar
Sabin, M. (2010) Fair tontine annuity. Available at SSRN 1579932.CrossRefGoogle Scholar
Weir, D.R. (1989) Tontines, public finance and revolution in France and England, 1688–1789. The Journal of Economic History, XLIX(1), 95–124.CrossRefGoogle Scholar
Yaari, M. (1965) Uncertain lifetime, life insurance, and the theory of the consumer. Review of Economic Studies, 32(2), 137–150.CrossRefGoogle Scholar