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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765793
• 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.

在过去的几十年中，死亡率已表现出巨大的改善。由于生活年金合同和养老金计划通常持续数十年，因此大多数发达国家逐渐增加寿命的趋势意味着年金提供者，退休计划以及养老金/长期护理系统因这种寿命的增加而面临很大的风险。另一方面，由于灾难的死亡率突然增加，人寿保险公司面临死亡率增加的风险。由于死亡率不确定性，人寿保险和年金提供者需要通过采用某些策略和/或购买死亡率与死亡率的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，以更好地定价人寿保险，年金产品，退休金/社会保障计划以及与死亡率联系的证券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，以及对死亡率进行建模的统计方法。统计方法的发展风险评估方法是我的研究计划的核心。特别是，我将：i）应用简单的回归统计数据来研究a）通过自然树篱通过自然树篱的死亡率免疫； ii）系统地将统计方法应用于单个人群和多个人群的死亡率建模。通过自然树篱（通过将死亡率和利益免疫接种对对冲的两种风险对冲风险的策略）是一种创新的方法，这是一种创新的方法，这是一种创新的方法。这种可行的方法将帮助生活保险公司和年金提供商对冲不仅死亡率/寿命风险，还可以对冲利息风险。此外，由于其简单性，简单的线性回归方法在死亡率主题中具有更多的潜在应用。而且，使用简单回归的参数的估计值将为金融机构提供一种有效而简单的方法，以建模人口基础风险，依赖性和寿命/死亡率掉期。此外，我将系统地将统计方法应用于单个人群和多个人群的死亡率建模。统计方法包括贝叶斯概率理论，最少的绝对收缩和选择操作员，脊回归，詹姆斯 - 斯坦估计器，copula，时间序列，主成分分析，功能数据分析等。这些对死亡率建模的统计方法中的大多数先前尚未在精算文献中进行研究。拟议的研究旨在将这种新颖的方法应用于死亡率模型的研究，因此有可能为研究这些模型和死亡率和寿命风险的管理做出重大贡献。