Mortality risk: modelling, evaluation and risk management

死亡风险：建模、评估和风险管理

• 批准号: RGPIN-2014-04682
• 负责人: Liu, Xiaoming
• 金额: $ 0.8万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=587952
• 关键词: Mortality; risk; modelling; evaluation; management

Pensions are a top of mind issue as more and more reports discuss the potential huge deficit in Government social security and health systems, and the threat of bankruptcy in many union's retirement plans. One of the main culprits is the unprecedented and unanticipated increase in life expectancy. Although mortality prediction has been a traditional topic in actuarial science and demography, past experience shows that the causes of mortality improvement have not been well understood. Uncertainty in mortality changes has become a major challenge for government, insurance companies and pension planners in most countries. Stochastic mortality models may be used to study the impact of mortality risk on plans and products. This new perspective about mortality indicates that we need new models as well as new evaluation and risk management methodologies for mortality risk. My research is about these newly emerging research topics. My proposed research is both a continuation and an expansion of my current work and can be grouped into three broad areas of research projects. 1. Markovian mortality modelling approach and its applications a. In this study, we continue our work on developing biological-based mortality modelling and prediction approach. The biological-based aging process will be characterized using either direct information from physiological variables or indirect information about health such as medical expenditures at different ages to enhance the mortality modelling and improve predictions. The research outcome of this project will deepen our understanding on human aging and mortality improvement. The applications of our results will not only be in modelling mortality for life insurance and annuity pricing, but also for modeling health care needs and cost projection. b. While phase-type (PH) models are useful in many fields of application, it is notoriously difficult to obtain efficient parameter estimation for PH models. However, for special structured PH aging model, we normally can obtain analytic functional expression for the distribution, and this allows us to employ maximum likelihood method and fast Bayesian approach to obtain parametric estimation. Our objective in this area is to provide efficient estimation methods for data from different sources and customize the PH model for different application purposes. The outcome of this research will not only advance mortality studies but also facilitate the application of PH models in many other areas. 2: Generalized modelling framework for the valuation of mortality-linked products My research in this area is motivated by the emergence of many modern insurance products with option-embedded features. A generalized valuation framework needs to be developed where both insurance and financial risks are stochastically modelled and correlated. We consider regime-switching models for interest and mortality risks because it can provide a coherent structure for both risks and a flexible dependence relationship in this joint modelling framework. This generalized modelling framework will allow hybrid products containing both insurance and financial risks to be properly valuated. Our approach also contributes to the theory of developing bivariate models in which the dependence structure between two risks are allowed to change under different measures. 3. Risk management through mortality-indexed product design I propose a risk-sharing strategy between an annuity provider and its policyholders, in which the benefit of the products will be adjusted according to a longevity index designed to reflect the unexpected mortality changes. This type of product design may provide a economic solution for all parties that are affected by the financial consequence of longevity risk.

随着越来越多的报告讨论政府社会保障和卫生系统的潜在巨大赤字，以及许多工会退休计划中破产的威胁，养老金是头脑中的首要问题。主要罪魁祸首之一是预期寿命的前所未有且意外的增加。尽管死亡率预测一直是精算科学和人口统计学中的传统话题，但过去的经验表明，改善死亡率的原因尚未得到充分理解。死亡率变化的不确定性已成为大多数国家政府，保险公司和退休金计划者的主要挑战。随机死亡率模型可用于研究死亡风险对计划和产品的影响。关于死亡率的新观点表明，我们需要新的模型以及新的评估和风险管理方法论，以实现死亡风险。我的研究是关于这些新兴的研究主题。我提出的研究既是我当前工作的延续和扩展，并且可以分为三个广泛的研究项目。 1。马尔可夫死亡率建模方法及其应用 一个。 在这项研究中，我们继续在开发基于生物学的死亡率建模和预测方法方面的工作。基于生物学的老化过程将使用来自生理变量的直接信息或有关健康的间接信息（例如不同年龄的医疗支出）来表征，以增强死亡率建模并改善预测。该项目的研究结果将加深我们对人类衰老和死亡率改善的理解。我们的结果的应用不仅将在对人寿保险和年金定价的死亡率上进行建模，还将用于建模医疗保健需求和成本投影。 b。 尽管相类型（PH）模型在许多应用领域都有用，但众所周知，很难获得pH模型的有效参数估计。但是，对于特殊的结构化pH老化模型，我们通常可以获得分布的分析功能表达，这使我们能够采用最大的似然方法和快速贝叶斯方法来获得参数估计。我们在该领域的目标是为来自不同来源的数据提供有效的估计方法，并为不同的应用目的自定义pH模型。这项研究的结果不仅将提高死亡率研究，而且还将促进许多其他领域的pH模型的应用。 2：与死亡率连接产品估值的广义建模框架 我在这一领域的研究是出于许多现代保险产品具有期权功能的兴起。需要开发一个广义的估值框架，在随机建模和关联保险和财务风险的情况下。我们考虑了利息和死亡率风险的制度转换模型，因为它可以在此联合建模框架中为风险和灵活的依赖关系提供连贯的结构。这个广义的建模框架将使包含保险和财务风险的混合产品得到适当的评价。我们的方法还有助于开发双变量模型的理论，在这种模型中，在不同的措施下，允许两个风险之间的依赖性结构改变。 3。通过死亡率指数产品设计的风险管理 我提出了年金提供商与其保单持有人之间的风险分享策略，其中将根据旨在反映意外死亡率变化的寿命指数来调整产品的好处。这种类型的产品设计可能会为受长寿风险财务后果影响的所有当事方提供经济解决方案。