标题： 具有协整关系的长程依赖死亡率建模 显示英文标题

标题： Long-range dependent mortality modeling with cointegration

摘要： 公开可用的生命表实证研究发现了国家死亡率数据中的长程依赖性（LRD）。 尽管长寿市场应以国家的死亡率强度为基准，但保险公司更关注与其自身投资组合相关的死亡率强度，而不是国家层面的。 最近在死亡率建模方面的进展利用分数布朗运动（fBm）来捕捉LRD。 一种理论灵活的方法甚至考虑了混合分数布朗运动（mfBm）。 通过使用Volterra过程，我们证明了直接使用mfBm会遇到识别问题，因此保险公司很难从其投资组合中检测到LRD效应。 协整技术可以有效地将国家死亡率强度中的LRD信息引入到保险公司经验投资组合的死亡率模型中。 在开环均衡控制框架下，针对具有LRD的协整死亡率强度，推导出了显式且唯一的均衡长寿对冲策略。 使用推导出的对冲策略，我们的数值示例表明，估计协整关系的准确性对于对冲具有LRD国家死亡率强度的保险公司长寿风险至关重要。 显示英文摘要

摘要： Empirical studies with publicly available life tables identify long-range dependence (LRD) in national mortality data. Although the longevity market is supposed to benchmark against the national force of mortality, insurers are more concerned about the forces of mortality associated with their own portfolios than the national ones. Recent advances on mortality modeling make use of fractional Brownian motion (fBm) to capture LRD. A theoretically flexible approach even considers mixed fBm (mfBm). Using Volterra processes, we prove that the direct use of mfBm encounters the identification problem so that insurers hardly detect the LRD effect from their portfolios. Cointegration techniques can effectively bring the LRD information within the national force of mortality to the mortality models for insurers' experienced portfolios. Under the open-loop equilibrium control framework, the explicit and unique equilibrium longevity hedging strategy is derived for cointegrated forces of mortality with LRD. Using the derived hedging strategy, our numerical examples show that the accuracy of estimating cointegration is crucial for hedging against the longevity exposure of insurers with LRD national force of mortality.