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摘要翻译：
近年来，死亡衍生品市场开始发展，作为处理系统死亡风险的一种方式，系统死亡风险是人寿保险和年金合同中固有的。系统死亡风险是由于未来死亡强度的不确定发展，或{\IT危险率}。在本文中，我们发展了一个纯捐赠的定价理论，当套期保值与死亡率远期是允许的。与纯禀赋相关的危险率和预测死亡率的参考危险率是相关的，并用扩散过程建模。我们通过假设发行公司用远期死亡率对冲其合同，并要求以预先指定的瞬时夏普比率的形式对死亡率风险的不可对冲部分进行补偿，从而对纯捐赠进行定价。本文的主要结果是，当合同数目接近无穷大时，每合同的价值解一个线性偏微分方程。可以将极限价格表示为等价鞅测度下的期望。另一个重要的结果是，与没有套期保值的价格相比，用死亡率远期套期保值可能会提高或降低这种纯捐赠的价格，正如Bayraktar等人所确定的那样。[2009]。参考死亡率风险的市场价格和两个投资组合之间的相关性共同决定了套期保值的成本。我们用数值例子证明了我们的结果。
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英文标题：
《Hedging Pure Endowments with Mortality Derivatives》
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作者：
Ting Wang and Virginia R. Young
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最新提交年份：
2010
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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：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
In recent years, a market for mortality derivatives began developing as a way to handle systematic mortality risk, which is inherent in life insurance and annuity contracts. Systematic mortality risk is due to the uncertain development of future mortality intensities, or {\it hazard rates}. In this paper, we develop a theory for pricing pure endowments when hedging with a mortality forward is allowed. The hazard rate associated with the pure endowment and the reference hazard rate for the mortality forward are correlated and are modeled by diffusion processes. We price the pure endowment by assuming that the issuing company hedges its contract with the mortality forward and requires compensation for the unhedgeable part of the mortality risk in the form of a pre-specified instantaneous Sharpe ratio. The major result of this paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting price as an expectation under an equivalent martingale measure. Another important result is that hedging with the mortality forward may raise or lower the price of this pure endowment comparing to its price without hedging, as determined in Bayraktar et al. [2009]. The market price of the reference mortality risk and the correlation between the two portfolios jointly determine the cost of hedging. We demonstrate our results using numerical examples.
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PDF链接：
https://arxiv.org/pdf/1011.0248
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