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.

即使过去死亡率提高的趋势经历了数次永久性变化，但在对长寿挂钩证券进行定价时，有关未来死亡率趋势的不确定性通常仍然无法建模。在本文中，我们提出了一个与长寿挂钩证券估值的随机建模框架，该框架明确考虑了长期死亡率趋势中未来随机变化的风险。我们构建了一组有意义的概率失真，这些失真暗示了在保留基本模型结构的前提下进行了等效的风险调整定价方法。受（再）保险公司基于风险的资本要求的启发，我们还建立了一种资本成本定价方法，然后该方法将作为适当的参考框架，为长寿风险的市场价格找到一个合理的范围。在数值应用中