Optimal Retirement Tontines for the 21st Century: With Reference to Mortality Derivatives in 1693
AbstractHistorical tontines promised enormous rewards to the last survivors at the expense of those who died early. While this design appealed to the gambling instinct, it is a suboptimal way to manage longevity risk during retirement. This is why fair life annuities making constant payments -- where the insurance company is exposed to the longevity risk -- induces greater lifetime utility. However, tontines do not have to be designed using a winner-take-all approach and insurance companies do not actually sell fair life annuities, partially due to aggregate longevity risk. In this paper we derive the tontine structure that maximizes lifetime utility, but doesn't expose the sponsor to any longevity risk. We examine its sensitivity to the size of the tontine pool; individual longevity risk aversion; and subjective health status. The optimal tontine varies with the individual's longevity risk aversion $\gamma$ and the number of participants $n$, which is problematic for product design. That said, we introduce a structure called a natural tontine whose payout declines in exact proportion to the (expected) survival probabilities, which is near-optimal for all $\gamma$ and $n$. We compare the utility of optimal tontines to the utility of loaded life annuities under reasonable demographic and economic conditions and find that the life annuity's advantage over tontines, is minimal. We also review and analyze the first-ever mortality-derivative issued by the British government, known as King Williams's tontine of 1693. We shed light on the preferences and beliefs of those who invested in the tontines vs. the annuities and argue that tontines should be re-introduced and allowed to co-exist with life annuities. Individuals would likely select a portfolio of tontines and annuities that suit their personal preferences for consumption and longevity risk, as they did over 320 years ago.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1307.2824.
Date of creation: Jul 2013
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-07-15 (All new papers)
- NEP-DEM-2013-07-15 (Demographic Economics)
- NEP-HIS-2013-07-15 (Business, Economic & Financial History)
- NEP-RMG-2013-07-15 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Nicholas C. Barberis, 2013. "Thirty Years of Prospect Theory in Economics: A Review and Assessment," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 173-96, Winter.
- Alexis Direr, 2010.
"Flexible Life Annuities,"
Journal of Public Economic Theory,
Association for Public Economic Theory, vol. 12(1), pages 43-55, 02.
- Cannon, Edmund & Tonks, Ian, 2008. "Annuity Markets," OUP Catalogue, Oxford University Press, number 9780199216994.
- Adam Creighton & Henry Hongbo Jin & John Piggott & Emiliano A. Valdez, 2005. "Longevity Insurance: A Missing Market," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 50(sp), pages 417-435.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.