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

长寿/死亡风险的对冲和死亡率建模的统计方法

• 批准号: RGPIN-2019-06782
• 负责人: Tsai, CaryChiLiang
• 金额: $ 1.31万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=716085
• 关键词: Hedging; longevity; mortality; risks; statistical

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.

在过去的几十年里，死亡率有了显着的改善。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寿命延长带来的重大风险。另一方面，由于灾难造成的死亡率突然上升，人寿保险公司面临着死亡率上升的风险。由于死亡的不确定性，人寿保险和年金提供商需要通过采取一些策略和/或购买与死亡相关的证券来对冲死亡和长寿风险。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挂钩证券定价是一项非常紧迫的任务。 拟议的研究计划涉及对冲长寿和死亡风险以及死亡率建模的统计方法。风险评估统计方法的发展是我研究项目的核心。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-利息免疫，以及 b) 人口基础风险和依赖性建模，c) 寿命/死亡率互换，以及 d) 队列死亡率；和 II) 系统地应用统计方法来模拟单个人群和多个人群的死亡率。 通过自然对冲（一种对冲受某些因素变化产生相反影响的两种风险的策略），通过结合死亡率和利息免疫来进行死亡利息免疫是一种创新方法。这种可行的方法将帮助人寿保险公司和年金提供商不仅对冲死亡/长寿风险，而且还对冲利息风险。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且简单的方法来对人口基础风险、依赖性和寿命/死亡率互换进行建模。 此外，我将系统地应用统计方法来模拟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估计器、copula、时间序列、主成分分析、函数数据分析等。 大多数死亡率建模的统计方法此前并未在精算文献中进行过研究。拟议的研究旨在将这种新颖的方法应用于死亡模型的研究，因此有可能为这些模型的研究以及死亡和长寿风险的管理做出重大贡献。