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ON THE OPTIMAL COMBINATION OF ANNUITIES AND TONTINES

Published online by Cambridge University Press:  31 January 2020

An Chen ,
Manuel Rach  and
Thorsten Sehner Open the ORCID record for Thorsten Sehner [Opens in a new window]
An Chen
Affiliation:
Institute of Insurance Science Ulm UniversityHelmholtzstraβe 20 89069 Ulm, Germany E-Mail: [email protected]
Manuel Rach*
Affiliation:
Institute of Insurance Science Ulm UniversityHelmholtzstraβe 20 89069 Ulm, Germany E-Mail: [email protected]
Thorsten Sehner
Affiliation:
Institute of Insurance Science Ulm UniversityHelmholtzstraβe 20 89069 Ulm, Germany E-Mail: [email protected]
*
E-Mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

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Tontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines can be combined to form a retirement plan which is cheaper than an annuity, but provides a less volatile retirement income than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: the previously introduced “tonuity”, a product very similar to the tonuity which we call “antine” and a portfolio consisting of an annuity and a tontine. We show that the payoffs of a tonuity and an antine can be replicated by a portfolio consisting of an annuity and a tontine. Consequently, policyholders achieve higher expected utility levels when choosing the portfolio over the novel retirement products tonuity and antine. Further, we derive conditions on the premium loadings of annuities and tontines indicating when the optimal portfolio is investing a positive amount in both annuity and tontine, and when the optimal portfolio turns out to be a pure annuity or a pure tontine.

Keywords

Optimal retirement productsannuitytontinetonuityantineG22J32
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 95 - 129
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
© Astin Bulletin 2020

References

Bauer, D. and Weber, F. (2008) Assessing investment and longevity risks within immediate annuities. Asia-Pacific Journal of Risk and Insurance, 3(1), 89–111.CrossRefGoogle Scholar
Bernhardt, T. and Donnelly, C. (2019) Modern tontine with bequest: Innovation in pooled annuity products. Insurance: Mathematics and Economics, 86, 168–188.Google Scholar
Brown, J.R. (2007) Rational and behavioral perspectives on the role of annuities in retirement planning. Technical report, National Bureau of Economic Research.CrossRefGoogle Scholar
Cairns, A.J. (2013) Robust hedging of longevity risk. Journal of Risk and Insurance, 80(3), 621–648.CrossRefGoogle Scholar
Caliendo, F.N., Gorry, A. and Slavov, S. (2017) Survival ambiguity and welfare. Technical report, National Bureau of Economic Research.CrossRefGoogle Scholar
Chen, A., Haberman, S. and Thomas, S. (2018) The implication of the hyperbolic discount model for the annuitisation decisions. Journal of Pension Economics & Finance, 1–20.Google Scholar
Chen, A., Hieber, P. and Klein, J.K. (2019) Tonuity: A novel individual-oriented retirement plan. ASTIN Bulletin: The Journal of the IAA, 49(1), 5–30.CrossRefGoogle Scholar
Chen, A. and Rach, M. (2019) Options on tontines: An innovative way of combining annuities and tontines. Insurance: Mathematics and Economics, 89, 182–192.Google Scholar
Davidoff, T., Brown, J.R. and Diamond, P.A. (2005) Annuities and individual welfare. American Economic Review, 95(5), 1573–1590.CrossRefGoogle 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
Gottlieb, D. (2012) Prospect theory, life insurance, and annuities. The Wharton School Research Paper No. 44.Google Scholar
Gumbel, E. (1958) Statistics of Extremes. New York: Columbia University Press.CrossRefGoogle Scholar
Hu, W.-Y. and Scott, J.S. (2007) Behavioral obstacles in the annuity market. Financial Analysts Journal, 63(6), 71–82.CrossRefGoogle Scholar
Inkmann, J., Lopes, P. and Michaelides, A. (2010) How deep is the annuity market participation puzzle? The Review of Financial Studies, 24(1), 279–319.CrossRefGoogle Scholar
Kling, A., Russ, J. and Schilling, K. (2014) Risk analysis of annuity conversion options in a stochastic mortality environment. ASTIN Bulletin: The Journal of the IAA, 44(2), 197–236.CrossRefGoogle Scholar
Li, J.S.-H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177–200.CrossRefGoogle Scholar
Li, Y. and Rothschild, C. (2019) Selection and redistribution in the irish tontines of 1773, 1775, and 1777. Journal of Risk and Insurance.Google Scholar
Lin, Y. and Cox, S.H. (2005) Securitization of mortality risks in life annuities. Journal of Risk and Insurance, 72(2), 227–252.CrossRefGoogle Scholar
Milevsky, M.A. (2013) Life Annuities: An Optimal Product for Retirement Income. Charlottesville: CFA Institute.Google Scholar
Milevsky, M.A. (2015) King William's Tontine: Why the Retirement Annuity of the Future Should Resemble Its Past. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Milevsky, M.A. and Salisbury, T.S. (2015) Optimal retirement income tontines. Insurance: Mathematics and Economics, 64, 91–105.Google Scholar
Milevsky, M.A. and Salisbury, T.S. (2016) Equitable retirement income tontines: Mixing cohorts without discriminating. ASTIN Bulletin: The Journal of the IAA, 46(3), 571–604.CrossRefGoogle Scholar
Mitchell, O.S. (2002) Developments in decumulation: The role of annuity products in financing retirement. In Ageing, Financial Markets and Monetary Policy (eds. A.J. Auerbach and H. Herrmann), pp. 97–125. Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
O'Dea, C. and Sturrock, D. (2019) Survival pessimism and the demand for annuities. Technical report, Institute for Fiscal Studies.Google Scholar
Olivieri, A. and Pitacco, E. (2019) Linking annuity benefits to the longevity experience: A general framework. Available at SSRN: https://ssrn.com/abstract=3326672.CrossRefGoogle Scholar
Peijnenburg, K., Nijman, T. and Werker, B.J. (2016) The annuity puzzle remains a puzzle. Journal of Economic Dynamics and Control, 70, 18–35.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
Poppe-Yanez, G. (2017) Mortality learning and optimal annuitization. Working paper. Available at https://www.gc.cuny.edu/CUNY_GC/media/CUNY-Graduate-Center/PDF/Programs/Economics/Other%20docs/mortannui.pdf.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
Royal London (2018) Will we ever summit the pension mountain? Technical report, Royal London Mutual Insurance Society Limited.Google Scholar
Sabin, M.J. (2010) Fair tontine annuity. Available at SSRN: https://ssrn.com/abstract=1579932.CrossRefGoogle Scholar
Statista (2019) Average risk-free investment rate in germany 2015-2019. Available at https://www.statista.com/statistics/885774/average-risk-free-rate-germany/; accessed on October 23, 2019.Google Scholar
Weinert, J.-H. and Gründl, H. (2017) The modern tontine: An innovative instrument for longevity risk management in an aging society. Available at SSRN: https://ssrn.com/abstract=3088527.CrossRefGoogle Scholar
Yaari, M.E. (1965) Uncertain lifetime, life insurance, and the theory of the consumer. The Review of Economic Studies, 32(2), 137–150.CrossRefGoogle Scholar
Yagi, T. and Nishigaki, Y. (1993) The inefficiency of private constant annuities. Journal of Risk and Insurance, 60(3), 385–412.CrossRefGoogle Scholar
Young, V.R. (2014) Premium principles. Wiley StatsRef: Statistics Reference Online.CrossRefGoogle Scholar