Hedging of longevity/mortality risks and statistical approaches to modelling mortality rates

在过去的几十年里，死亡率出现了戏剧性的改善。由于人寿年金合同和养老金计划通常持续数十年，大多数发达国家的预期寿命逐渐延长的趋势意味着，年金提供者、退休计划和养老金/长期护理系统面临着这种延长寿命的重大风险。另一方面，人寿保险公司面临着由于灾难死亡率突然上升而导致死亡率上升的风险。由于死亡率的不确定性，人寿保险和年金提供者需要通过采取一些策略和/或购买与死亡率挂钩的证券来对冲死亡率和长寿风险。此外，建立有效的死亡率模型以提供准确的死亡率，以更好地定价人寿保险、年金产品、养老金/社会保障计划和与死亡率挂钩的证券，是一件非常紧迫的事情。*拟议的研究计划涉及对冲寿命和死亡率风险，以及建模死亡率的统计方法。开发风险评估的统计方法是我研究计划的核心。具体地说，我将：*i)应用简单的回归统计来研究a)通过自然对冲进行死亡率-利息免疫，并对b)总体基本风险和依赖性、c)寿命/死亡率互换和d)队列死亡率进行建模；以及*ii)系统地应用统计方法对单个人口和多个人口的死亡率进行建模。*通过自然对冲(一种对冲受某些因素变化影响相反的两种风险的策略)进行死亡率-利息免疫是一种创新的方法。这一可行的方法将帮助寿险公司和年金提供者不仅对冲死亡/长寿风险，还将对冲利息风险。此外，由于其简单性，简单的线性回归方法在死亡率问题上有更多的潜在应用。而且，使用简单回归参数的估计将为金融机构提供一种有效和简单的方法来建模总体基础风险、相关性和寿命/死亡率互换。此外，我还将系统地应用统计方法来建模单个人群和多个人群的死亡率。统计方法包括贝叶斯概率论、最小绝对收缩和选择算子、岭回归、James-Stein估计量、Copula、时间序列、主成分分析、函数数据分析等。拟议的研究旨在将这一新方法应用于死亡率模型的研究，因此，有可能对这些模型的研究以及死亡率和长寿风险的管理做出重大贡献。

Over past decades, mortality rates have displayed dramatic improvement. Because life annuity contracts and pension plans often last for decades, the trend in most developed countries toward a gradual increase in life expectancy means that annuity providers, retirement programs, and pension/long-term care systems face significant risk from this increased longevity. On the other hand, life insurers face risk from increased mortality due to a sudden rise in mortality from catastrophes. As a result of mortality uncertainty, life insurance and annuity providers need to hedge mortality and longevity risks by adopting some strategies and/or buying mortality-linked securities. Moreover, building effective mortality models to provide accurate mortality rates for better pricing of life insurance, annuity products, pension/social security plans, and mortality-linked securities is a matter of great urgency.******The proposed research program pertains to hedging longevity and mortality risks, and statistical approaches to modeling mortality rates. The development of statistical approaches to risk assessment is the core of my research program. In particular, I will: ******I) Apply simple regression statistics to study a) mortality-interest immunization via natural hedge, and modeling of b) population basis risk and dependence, c) longevity/mortality swaps, and d) cohort mortality rates; and******II) Systematically apply statistical approaches to modeling mortality rates for a single population and multiple populations.******Mortality-interest immunization via natural hedge (a strategy of hedging two risks affected oppositely by a change in some factor) by combining mortality and interest immunizations is an innovative approach. This feasible method will help life insurers and annuity providers hedge not only mortality/longevity risks, but also interest risk. In addition, due to its simplicity, the simple linear regression approach has more potential applications in mortality topics. And, using the estimates of parameters of the simple regression will provide financial institutions with an effective and easy way of modeling the population basis risk, the dependence, and the longevity/mortality swaps.******Furthermore, I will systematically apply statistical approaches to modeling mortality rates for a single population and multiple populations. The statistical methods include Bayesian probability theory, least absolute shrinkage and selection operator, ridge regression, James-Stein estimator, copula, time series, principal component analysis, functional data analysis, and others.******Most of these statistical approaches to modeling mortality rates have not been investigated previously in the actuarial literature. The proposed research aims to apply this novel approach to the study of mortality models and thus, has the potential to make significant contributions to the study of these models and management of mortality and longevity risks.**