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

在过去几十年中，死亡率有了显著改善。由于终身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增加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寿命增加的重大风险。另一方面，寿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，寿险和年金提供商需要通过采取一些策略和/或购买死亡率相关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，从而更好地为人寿保险、年金产品、养老金/社会保障计划和死亡率相关证券定价，这是一个非常紧迫的问题。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。风险评估的统计方法的发展是我的研究计划的核心。特别是，我将：I）应用简单回归统计来研究a）通过自然对冲的死亡率利益免疫，以及B）群体基础风险和依赖性的建模，c）寿命/死亡率互换，以及d）队列死亡率;以及II）系统地应用统计方法来建模单个群体和多个群体的死亡率。通过自然对冲（一种对冲两种风险的策略）将死亡率免疫和利息免疫相结合的方法是一种创新的方法。这种可行的方法将有助于寿险公司和年金提供商不仅对冲死亡率/长寿风险，而且对冲利率风险。此外，由于简单线性回归方法的简单性，它在死亡率方面有更多的潜在应用。而且，使用简单回归的参数估计将为金融机构提供一种有效和简单的方法来建模人口基础风险、依赖性和寿命/死亡率互换。此外，我将系统地应用统计方法来建模死亡率为一个单一的人口和多个人口。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、Copula、时间序列、主成分分析、函数数据分析等。大多数这些统计方法来建模死亡率没有被调查以前在精算文献。拟议的研究旨在将这种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.