Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities

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dc.creatorBayraktar, Erhan
dc.creatorMilevsky, Moshe
dc.creatorPromislow, David
dc.creatorYoung, Virginia
dc.date2008-02-22
dc.date.accessioned2026-07-07T12:10:28Z
dc.date.available2026-07-07T12:10:28Z
dc.descriptionWe develop a theory for valuing non-diversifiable mortality risk in an incomplete market. We do this 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 {\it identical} to the upper good deal bound of Cochrane and Saá-Requejo (2000) and of Björk and Slinko (2006) applied to our setting. A second result of our paper is that the value per contract solves a {\it 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 (as in Blanchet-Scalliet, El Karoui, and Martellini (2005)), and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.
dc.descriptionKeywords: Stochastic mortality; pricing; annuities; Sharpe ratio; non-linear partial differential equations; market price of risk; equivalent martingale measures
dc.identifierhttps://arxiv.org/abs/0802.3250
dc.identifierhttp://arxiv.org/abs/0802.3250
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209942
dc.subjectPricing of Securities
dc.subjectOptimization and Control
dc.subject91B30; 91B70
dc.titleValuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities
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