Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities

Erhan Bayraktar, Moshe Milevsky, S. David Promislow and Virginia R. Young

Journal of Economic Dynamics and Control, 2009, vol. 33, issue 3, 676-691

Abstract: We develop a theory for valuing non-diversifiable mortality risk in an incomplete market by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of our paper is that the value of the life annuity is identical to the upper good deal bound of Cochrane and Saá-Requejo [2000. Beyond arbitrage: good deal asset price bounds in incomplete markets. Journal of Political Economy 108, 79-119] and of Björk and Slinko [2006. Towards a general theory of good deal bounds. Review of Finance 10, 221-260] applied to our setting. A second result of our paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting value as an expectation with respect to an equivalent martingale measure, and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.

Keywords: Stochastic; mortality; Pricing; Annuities; Sharpe; ratio; Non-linear; partial; differential; equations; Market; price; of; risk; Equivalent; martingale; measures (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (27)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0165-1889(08)00162-0
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:33:y:2009:i:3:p:676-691

Access Statistics for this article

Journal of Economic Dynamics and Control is currently edited by J. Bullard, C. Chiarella, H. Dawid, C. H. Hommes, P. Klein and C. Otrok

More articles in Journal of Economic Dynamics and Control from Elsevier
Bibliographic data for series maintained by Catherine Liu ().