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摘要翻译：
我们发展了一个在不完全市场中定价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。我们证明了我们接下来的估值公式满足一些期望的性质。例如，我们表明它在卖出的合约数量中是次加性的。一个关键的结果是，如果危险率是随机的，那么风险调整后的生存概率大于物理生存概率，即使合同数量接近无穷大。
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英文标题：
《Financial Valuation of Mortality Risk via the Instantaneous Sharpe
Ratio: Applications to Pricing Pure Endowments》
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作者：
Moshe A. Milevsky, S. David Promislow, Virginia R. Young
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最新提交年份：
2007
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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：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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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 pricing 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 prove that our ensuing valuation formula satisfies a number of desirable properties. For example, we show that it is subadditive in the number of contracts sold. A key result is that if the hazard rate is stochastic, then the risk-adjusted survival probability is greater than the physical survival probability, even as the number of contracts approaches infinity.
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PDF链接：
https://arxiv.org/pdf/0705.1302
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