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，以便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，这是一个非常紧迫的问题。拟议的研究计划涉及对冲长寿和死亡风险，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。特别是，我将：i)应用简单的回归统计来研究a)通过自然对冲进行死亡率免疫，以及b)基于人口的风险和依赖性、c)寿命/死亡率互换和d)队列死亡率的建模；以及ii)系统地应用统计方法来模拟单个人口和多个人口的死亡率。通过将死亡率免疫和利息免疫结合起来，通过自然对冲(一种对冲因某些因素的变化而受到相反影响的两种风险的策略)进行的死亡兴趣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总体基础风险、相关性和寿命/死亡率掉期。此外，我将系统地应用统计学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估计量、Copula、时间序列、主成分分析、函数数据分析等。这些用于模拟死亡率的统计方法中的大多数以前在精算文献中都没有被研究过。这项研究旨在将这一新的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.