Mortality risk: modelling, evaluation and risk management

随着越来越多的报告讨论政府社会保障和医疗体系中潜在的巨额赤字，以及许多工会退休计划中的破产威胁，养老金成为人们首要考虑的问题。主要罪魁祸首之一是预期寿命史无前例的意外增长。虽然死亡率预测一直是精算学和人口学的一个传统话题，但过去的经验表明，死亡率改善的原因还没有被很好地理解。死亡率变化的不确定性已成为大多数国家政府、保险公司和养老金规划者面临的主要挑战。随机死亡率模型可用于研究死亡率风险对计划和产品的影响。这种关于死亡率的新观点表明，我们需要新的死亡风险模型以及新的评估和风险管理方法。我的研究是关于这些新兴的研究课题。我提出的研究是我目前工作的延续和扩展，可以分为三大研究领域。**1.马尔可夫死亡率建模方法及其应用*a.在这项研究中，我们继续开发基于生物的死亡率建模和预测方法。基于生物的衰老过程将使用来自生理变量的直接信息或关于健康的间接信息(如不同年龄的医疗费用)来表征，以加强死亡率建模和改进预测。该项目的研究成果将加深我们对人类老龄化和死亡率改善的理解。我们的结果将不仅应用于人寿保险和年金定价的死亡率建模，而且还用于建模医疗保健需求和成本预测。*b.虽然相型(PH)模型在许多应用领域都很有用，但众所周知，为PH模型获得有效的参数估计是困难的。然而，对于特殊结构的PH老化模型，我们通常可以得到分布的解析函数表达式，这使得我们可以使用极大似然法和快速贝叶斯方法来获得参数估计。我们在这方面的目标是为不同来源的数据提供有效的估计方法，并根据不同的应用目的定制PH值模型。这项研究的结果不仅将推进死亡率研究，还将促进PH模型在许多其他领域的应用。**2：死亡率相关产品估值的通用建模框架*我在这一领域的研究是受到许多具有期权嵌入特征的现代保险产品的出现的推动。需要制定一个普遍的估值框架，其中保险和金融风险都是随机建模和相互关联的。我们考虑利率和死亡风险的制度转换模型，因为它可以为这两种风险提供一个连贯的结构，并在这个联合建模框架中提供灵活的依赖关系。这一通用的建模框架将允许对同时包含保险和金融风险的混合产品进行适当估值。我们的方法还有助于开发双变量模型，在该模型中，两个风险之间的依赖结构可以在不同的衡量标准下改变。**3.通过死亡率指数产品设计的风险管理*我提出了年金提供者和其投保人之间的风险分担策略，其中产品的收益将根据旨在反映意外死亡率变化的寿命指数进行调整。这种类型的产品设计可以为受到长寿风险财务后果影响的各方提供一种经济解决方案。

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.