Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities
By Erhan Bayraktar, M. Milevsky, David Promislow, Virginia R. Young. 2008
60 citations recorded by the source corpus.
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 Sa\'{a}-Requejo (2000) and of Bj\"{o}rk 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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Citations in the corpus
- Pricing Mortality Securities with Correlated Mortality Indexes (2011, unknown): “Bayraktar et al. (2009) propose to compensate a mortality risk taker according to an “instantaneous Sharpe ratio,” which is defined as the additional return in excess of the risk-free rate divided by the standard deviation of a mortality portfolio after all diversifiable risk is hedged away.”
- Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2017, background): “ing models with dierent interest rates for borrowing and lending, see, e.g., [24, 53] for derivative pricing models incorporating the default risk of the issuer of the nancial derivative, see, e.g., [4, 5, 109] for models for the pricing of nancial derivatives on untradable underlyings such as nanci”
- On the pricing of longevity-linked securities (2010, background): “Nevertheless, the general consensus amongst practitioners appears to be that whilst a breakthrough is yet to come, “betting on the time of death is set”,1 and several investment banks such as JPMorgan or Goldman Sachs have installed trading desks for longevity risk.”