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摘要翻译：
我们发展了一个在不完全市场中评估非多样化死亡率风险的理论。我们这样做，假设公司发出死亡或有索赔要求以预先指定的瞬时夏普比率的形式对这种风险进行赔偿。我们应用我们的方法对终身年金进行估值。本文的一个结果是，终身年金的价值与Cochrane和Sa'a}-Requejo(2000)以及Bj'o}rk和Slinko(2006)的上界一致。本文的第二个结果是，当契约数接近无穷大时，每个契约的值解一个{it线性}偏微分方程。人们可以将极限值表示为对等价鞅测度的期望（如Blanchet-Scalliet，El Karoui和Martellini(2005))，从这个表示中，人们可以将瞬时夏普比率解释为年金市场的死亡风险价格。
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英文标题：
《Valuation of Mortality Risk via the Instantaneous Sharpe Ratio:
Applications to Life Annuities》
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作者：
Erhan Bayraktar, Moshe Milevsky, David Promislow, Virginia Young
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/0802.3250
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