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

在过去的几十年里，死亡率有了显著的改善。由于终身年金合同和养老金计划通常持续数十年，在大多数发达国家，预期寿命逐渐增加的趋势意味着年金提供商、退休计划和养老金/长期护理系统面临着寿命延长带来的重大风险。另一方面，由于灾难死亡率的突然上升，寿险公司面临着死亡率上升的风险。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寿命风险。此外，建立有效的死亡率模型以提供准确的死亡率，以便更好地为人寿保险、年金产品、养老金/社会保障计划和与死亡率挂钩的证券定价，是一项非常紧迫的事项。******提出的研究计划涉及对冲寿命和死亡率风险，以及死亡率建模的统计方法。发展风险评估的统计方法是我研究计划的核心。特别是，我将：******I)应用简单的回归统计来研究a)通过自然对冲的死亡率-利息免疫，以及b)人口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******二)系统地应用统计方法对单一人口和多个人口的死亡率进行建模。******将死亡率和利息免疫结合起来，通过自然对冲（一种对冲某些因素变化相反影响的两种风险的策略）进行死亡率-利息免疫是一种创新方法。这种可行的方法不仅可以帮助寿险公司和年金提供商对冲死亡/寿命风险，还可以对冲利息风险。此外，由于其简单性，简单线性回归方法在死亡率主题中具有更多的潜在应用。并且，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基于人群的风险，依赖性和寿命/死亡率互换。******此外，我将系统地应用统计方法对单一人口和多个人口的死亡率进行建模。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、功能数据分析等。******这些死亡率建模的统计方法在以前的精算文献中没有被研究过。本研究旨在将这种新方法应用于死亡率模型的研究，从而有可能对这些模型的研究以及死亡率和寿命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.**