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arXiv · 0802.3250

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

Erhan Bayraktar·Moshe Milevsky·David Promislow·Virginia Young
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Abstract

We 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.

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Erhan Bayraktar, Moshe Milevsky, David Promislow, Virginia Young. 2008-02-22. Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities. https://arxiv.org/abs/0802.3250

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