Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-23T01:49:06.890Z Has data issue: false hasContentIssue false
  • English
  • Français

Linking annuity benefits to the longevity experience: alternative solutions

Published online by Cambridge University Press:  17 January 2020

Annamaria Olivieri  and
Ermanno Pitacco
Annamaria Olivieri*
Affiliation:
1Department of Economics and Management, University of Parma, Italy
Ermanno Pitacco
Affiliation:
2DEAMS, University of Trieste, Italy
*
*Corresponding author. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The uncertainty regarding financial returns and the life expectancy, joint to the reduced social security benefits, increasingly expose individuals to the risk of outliving their post-retirement assets. However, the demand for longevity guarantees remains low, due to high costs. The providers, on their side, may be reluctant to offer non-adjustable longevity guarantees, as the risk is long term and difficult to predict. It is therefore convenient to reconsider the design of longevity guarantees. In particular, a participating structure, providing a link to some longevity experience, could allow a sharing of losses, and possibly profits, resulting in a reduction of the cost of the retained guarantee. The literature review suggests a number of alternatives to define a longevity-linking arrangement, but the topic is not yet completely explored. It is useful, in particular, to have a common framework, under which the various solutions can be interpreted and compared, also with a view to the trade-off between the retained risk and the cost of the guarantee. Developing a general structure describing longevity-linked post-retirement benefits is the main purpose of this paper. Allowing for aggregate longevity risk, we then examine suitable solutions for insurance products.

Keywords

Longevity-linked annuitiesLongevity risk participating annuitiesAggregate longevity riskLongevity guarantee
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 2 , September 2020 , pp. 316 - 337
Copyright
© Institute and Faculty of Actuaries 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bacinello, A.R., Millossovich, P.&Chen, A. (2018). The impact of longevity and investment risk on a portfolio of life insurance liabilities. European Actuarial Journal, 8, 257–290.CrossRefGoogle Scholar
Baker, T.&Siegelman, P. (2010). Tontines for the invincibles: enticing low risks into the health insurance pool with an idea from insurance history and behavioral economics. Wisconsin Law Review, 2010, 79–120.Google Scholar
Biffis, E. (2005). Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics, 37, 443–468.Google Scholar
Blackburn, C., Hanewald, K., Olivieri, A.&Sherris, M. (2017). Longevity risk management and shareholder value for a life annuity business. ASTIN Bulletin, 47, 43–77.CrossRefGoogle Scholar
Blackburn, C.&Sherris, M. (2013). Consistent dynamic affine mortality models for longevity risk applications. Insurance: Mathematics and Economics, 53, 64–73.Google Scholar
Bravo, J.M.&de Freitas, N.E.M. (2018). Valuation of longevity-linked life annuities. Insurance: Mathematics and Economics, 78, 212–229.Google Scholar
Brouhns, N., Denuit, M.&Vermunt, J. (2002). A Poisson log-bilinear regression approach to the construction of projected life tables. Insurance: Mathematics and Economics, 31, 373–393.Google Scholar
Cairns, A., Blake, D.&Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73, 687–718.CrossRefGoogle Scholar
Chen, A., Hieber, P.&Klein, J.K. (2019). Tonuity: a novel individual-oriented retirement plan. ASTIN Bulletin, 49, 5–30.CrossRefGoogle Scholar
Denuit, M., Haberman, S.&Renshaw, A. (2011). Longevity-indexed life annuities. North American Actuarial Journal, 15, 97–111.CrossRefGoogle Scholar
Denuit, M., Haberman, S.&Renshaw, A. (2015). Longevity-contingent deferred life annuities. Journal of Pension Economics and Finance, 14, 315–327.CrossRefGoogle Scholar
Donnelly, C. (2015). Actuarial fairness and solidarity in pooled annuity funds. ASTIN Bulletin, 45, 49–74.CrossRefGoogle Scholar
Donnelly, C., Guillén, M.&Nielsen, J.P. (2013). Exchanging uncertain mortality for a cost. Insurance: Mathematics and Economics, 52, 65–76.Google Scholar
Donnelly, C., Guillén, M.&Nielsen, J.P. (2014). Bringing cost transparency to the life annuity market. Insurance: Mathematics and Economics, 56, 14–27.Google Scholar
Hanbali, H., Denuit, M., Dhaene, J.&Trufin, J. (2019). A dynamic equivalence principle for systematic longevity risk management. Insurance: Mathematics and Economics, 86, 158–167.Google Scholar
Lee, R.&Carter, L. (1992). Modelling and forecasting US mortality. Journal of the American Statistical Association, 87, 659–675.Google Scholar
Lusardi, A. (2019). Financial literacy and the need for financial education: evidence and implications. Swiss Journal of Economics and Statistics, 155, 1.CrossRefGoogle Scholar
Lüthy, H., Keller, P.L., Bingswanger, K.&Gmür, B. (2001). Adaptive algorithmic annuities. Mitteilungen der Schwizerischen Aktuarvereinigung, 2/2001, 123–138.Google Scholar
Maurer, R., Mitchell, O.S., Rogalla, R.&Kartashov, V. (2013). Lifecycle portfolio choice with systematic longevity risk and variable investment-linked deferred annuities. The Journal of Risk and Insurance, 80, 649–676.CrossRefGoogle Scholar
McKeever, K. (2009). A short history of tontines. Fordham Journal of Corporate and Financial Law, 15, 491–521.Google Scholar
Milevsky, M.A. (2014). Portfolio choice and longevity risk in the late Seventeenth century: a re-examination of the first English tontine. Financial History Review, 21, 225–258.CrossRefGoogle Scholar
Milevsky, M.A.&Salisbury, T.S. (2015). Optimal retirement income tontines. Insurance: Mathematics and Economics, 64, 91–105.Google Scholar
Milevsky, M.A.&Salisbury, T.S. (2016). Equitable retirement income tontines: mixing cohorts without discriminating. ASTIN Bulletin, 46, 571–604.CrossRefGoogle Scholar
Olivieri, A.&Pitacco, E. (2009). Stochastic mortality: the impact on target capital. ASTIN Bulletin, 39, 541–563.CrossRefGoogle Scholar
Piggott, J., Valdez, E.A.&Detzel, B. (2005). The simple analytics of a pooled annuity fund. The Journal of Risk and Insurance, 72, 497–520.CrossRefGoogle Scholar
Pitacco, E., Denuit, M., Haberman, S.&Olivieri, A. (2009). Modelling Longevity Dynamics for Pensions and Annuity Business. Oxford University Press, Oxford.Google Scholar
Qiao, C.&Sherris, M. (2012). Managing systematic mortality risk with group self-pooling and annuitization schemes. The Journal of Risk and Insurance, 80, 949–974.CrossRefGoogle Scholar
Renshaw, A.&Haberman, S. (2003). Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33, 255–272.Google Scholar
Renshaw, A.&Haberman, S. (2006). A cohort-based extension of the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556–570.Google Scholar
Richter, A.&Weber, F. (2011). Mortality-Indexed annuities. Managing longevity risk via product design. North American Actuarial Journal, 15, 212–236.CrossRefGoogle Scholar
Sabin, M.J. (2010). Fair tontine annuity. Available at SSRN.com (http://ssrn.com/abstract=1579932).Google Scholar
Schrager, D. (2006). Affine stochastic mortality. Insurance: Mathematics and Economics, 38, 81–97.Google Scholar
Stamos, M.Z. (2008). Optimal consumption and portfolio choice for pooled annuity funds. Insurance: Mathematics and Economics, 43, 56–68.Google Scholar
Valdez, E.A., Piggott, J.&Wanga, L. (2006). Demand and adverse selection in a pooled annuity fund. Insurance: Mathematics and Economics, 39, 251–266.Google Scholar
Weinert, J.H.&Gründl, H. (2016). The modern tontine: an innovative instrument for longevity risk management in an aging society. Working Paper Series 22/2016, ICIR.Google Scholar