Even though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.

中文翻译：

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在死亡率趋势变化的情况下定价长寿挂钩证券

尽管死亡率改善的趋势在过去经历了几次永久性变化，但在为长寿相关证券定价时，关于未来死亡率趋势的不确定性通常没有被建模。在本文中，我们提出了一个用于评估长寿相关证券的随机建模框架，该框架明确考虑了长期死亡率趋势未来随机变化的风险。我们构建了一组有意义的概率扭曲，这意味着在保留基本模型结构的情况下，等效的风险调整定价措施。受（再）保险公司基于风险的资本要求的启发，我们还建立了资本成本定价方法，然后作为适当的参考框架，为长寿风险的市场价格寻找合理的范围。在数值应用中，