Mortality risk: modelling, evaluation and risk management

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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.