发表机构
Hong Kong University of Science and Technology (Guangzhou); University of Waterloo; Beijing Normal-Hong Kong Baptist University（香港科技大学（广州）; 滑铁卢大学; 北京师范大学-香港浸会大学联合国际学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种结合分数Lévy过程与布朗运动的随机死亡率模型，以捕捉长期依赖性，并开发奇异值分解近似方案实现长寿衍生品的高效定价。
AI 中文摘要
大量经验证据表明，忽略长期依赖性的随机死亡率模型往往会低估预期寿命，这可能对养老金计划和资金安排产生深远影响。本文通过分数Lévy过程与标准布朗运动的混合来建模随机死亡率。我们的随机死亡率模型在精算估值中具有良好的解析可处理性，并且在底层Lévy规格选择上具有灵活性。我们模型中嵌入的长期依赖性特征在关于第二次世界大战和COVID-19期间死亡率冲击的实证研究中得到了充分体现。为了对长寿衍生品进行高效数值定价，我们构建了一种有效的奇异值分解近似方案，以克服分数Lévy过程的非马尔可夫性带来的计算挑战。通过有效的残差校正方案，可以减少奇异值分解近似中的截断误差。
英文摘要
A substantial body of empirical evidence suggests that stochastic mortality models ignoring long range dependence tend to underestimate life expectancy, which may lead to profound implications for pension schemes and funding arrangements. This paper addresses the modelling of stochastic mortality via a mixture of a fractional Lévy process and standard Brownian motion. Our stochastic mortality model exhibits nice analytical tractability in actuarial valuations and flexibility in the choice of underlying Lévy specifications. The long range dependence feature embedded in our stochastic mortality model is well reflected in our empirical studies on the mortality shocks during World War II and COVID-19. For efficient numerical pricing of longevity derivatives, we construct an effective singular value decomposition approximation scheme to overcome the computational challenges arising from the non-Markovian nature of the fractional Lévy process. Truncation errors in singular value decomposition approximation can be reduced by an effective residual correction scheme.
