Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio
AbstractWe provide an overview of how the law of large numbers breaks down when pricing life-contingent claims under stochastic as opposed to deterministic mortality (probability, hazard) rates. In a stylized situation, we derive the limiting per-policy risk and show that it goes to a non-zero constant. This is in contrast to the classical situation when the underlying mortality decrements are known with certainty, per policy risk goes to zero. We decompose the standard deviation per policy into systematic and non-systematic components, akin to the analysis of individual stock (equity) risk in a Markowitz portfolio framework. Finally, we draw upon the financial analogy of the Sharpe Ratio to develop a premium pricing methodology under aggregate mortality risk. Copyright The Journal of Risk and Insurance, 2006.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by The American Risk and Insurance Association in its journal Journal of Risk & Insurance.
Volume (Year): 73 (2006)
Issue (Month): 4 ()
Contact details of provider:
Web page: http://www.wiley.com/bw/journal.asp?ref=0022-4367&site=1
More information through EDIRC
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- De Waegenaere, A.M.B. & Melenberg, B. & Stevens, R., 2010.
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-4578387, Tilburg University.
- Erhan Bayraktar & Moshe Milevsky & David Promislow & Virginia Young, 2008.
"Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities,"
- Bayraktar, Erhan & Milevsky, Moshe A. & David Promislow, S. & Young, Virginia R., 2009. "Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 676-691, March.
- Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
- Huang, Rachel J. & Tsai, Jeffrey T. & Tzeng, Larry Y., 2008. "Government-provided annuities under insolvency risk," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 377-385, December.
- Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Papers 0908.3196, arXiv.org.
- Helena Aro, 2013. "Systematic and non-systematic mortality risk in pension portfolios," Papers 1307.8020, arXiv.org, revised Jul 2013.
- Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.