随机死亡率下基于瞬时夏普比率的寿险定价：定理与证明
Pricing Life Insurance under Stochastic Mortality via the Instantaneous Sharpe Ratio: Theorems and Proofs
摘要：
假设保险公司要求以预先指定的瞬时夏普比率的形式补偿其风险，在不完全市场中建立了随机死亡率下的人寿保险定价规则.我们的估值公式满足一些理想的属性，其中许多是与标准差溢价原则。本文的主要结果是，当合同数量趋于无穷大时，每份合同的价格解一个线性偏微分方程。人们可以将极限价格解释为关于等价鞅测度的期望。另一个重要的结果是，如果风险率是随机的，那么风险调整后的保费大于净保费，即使合同的数量接近无穷大。我们提出了一个数值例子来说明我们的结果，以及相应的算法。
英文摘要：
We develop a pricing rule for life insurance under stochastic mortality in an incomplete market by assuming that the insurance company requires compensation for its risk in the form of a pre-specified instantaneous Sharpe ratio. Our valuation formula satisfies a number of desirable properties, many of which it shares with the standard deviation premium principle. The major result of the paper is that the price per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can interpret the limiting price as an expectation with respect to an equivalent martingale measure. Another important result is that if the hazard rate is stochastic, then the risk-adjusted premium is greater than the net premium, even as the number of contracts approaches infinity. We present a numerical example to illustrate our results, along with the corresponding algorithms.
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