Financial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product’s payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent contracts. As hybrid life insurance contracts depend on both financial and insurance risks, their valuation requires a hybrid valuation principle that combines the two concepts of financial and actuarial valuation. The aim of this paper is to present a novel three-step projection algorithm to valuate hybrid contracts by decomposing their payoff in three parts: a financial, hedgeable part, a diversifiable actuarial part, and a residual part that is neither hedgeable nor diversifiable. The first two parts of the resulting premium are directly linked to their corresponding hedging and diversification strategies, respectively. The method allows for a separate treatment of unsystematic, diversifiable mortality risk and systematic, aggregate mortality risk related to, for example, epidemics or population-wide improvements in life expectancy. We illustrate our method in the case of CAT bonds and a pure endowment insurance contract with profit and compare the three-step method to alternative valuation operators suggested in the literature.

中文翻译：

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采用新的三步法对人寿保险中的混合金融和精算产品进行估值

金融产品使用风险中性预期定价，通过对冲投资组合（尽可能准确）匹配产品的收益来证明其合理性。在保险中，保费计算是基于现实世界的最佳估计值加上风险溢价。保险风险溢价通常通过合并（在最好的情况下）独立合同来降低。由于混合型人寿保险合同既依赖于金融风险，也依赖于保险风险，因此它们的估值需要一种结合了金融估值和精算估值两个概念的混合估值原则。本文的目的是提出一种新颖的三步投影算法，通过将混合合约的收益分解为三个部分来评估它们：财务、可对冲部分、可多样化的精算部分和既不可对冲也不可多样化的剩余部分。所得溢价的前两部分分别与其相应的对冲和多元化策略直接相关。该方法允许对非系统性、可多样化的死亡风险和系统性、总体死亡风险进行单独处理，例如，与流行病或全人群预期寿命的提高有关。我们以 CAT 债券和具有利润的纯养老保险合同为例说明我们的方法，并将三步法与文献中建议的替代估值运营商进行比较。流行病或全人口预期寿命的改善。我们以 CAT 债券和具有利润的纯养老保险合同为例说明我们的方法，并将三步法与文献中建议的替代估值运营商进行比较。流行病或全人口预期寿命的改善。我们以 CAT 债券和具有利润的纯养老保险合同为例说明我们的方法，并将三步法与文献中建议的替代估值运营商进行比较。