通过瞬时夏普比率评估死亡风险：在人寿年金中的应用
Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities
摘要：
本文提出了一个在不完全市场中对不可分散的死亡率风险进行估值的理论。我们通过假设发行死亡或有索赔的公司要求以预先指定的瞬时夏普比率的形式对这种风险进行补偿来做到这一点。我们应用我们的方法来评估人寿年金。我们的论文的一个结果是，终身年金的价值与Cochrane和Saá-Requejo（2000）以及Björk和Slinko（2006）应用于我们的设置的上界相同。我们的论文的第二个结果是，当合约数量接近无穷大时，每份合约的价值解出了一个{ \it线性}偏微分方程。人们可以将极限值表示为关于等价鞅测度的期望值（如Blanchet-Scalliet，El Karoui和Martellini（2005）），并且从这种表示中，人们可以将瞬时夏普比率解释为年金市场的死亡率风险价格。
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 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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