Modeling of mortality rates, hedging of longevity and mortality risks, and pricing of mortality-linked securities

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Modeling the changes/dynamics of mortality rates is critical to the social benefit programs, solvency of life insurers, and the society as a whole. Mortality is a significant factor in shaping the population structure of a country that in turn affects the growth prospects of many industries. Retirement programs and long-term care systems need to consider the dynamics of mortality rates as well since incomes and benefit outgoes depend on mortality. Mortality is also one of the key factors in determining the premiums and reserves of life insurance and annuity products. Therefore, modeling of mortality is a very important issue. Evidence shows that human mortality rates improve gradually over the past decades. A failure to appropriately measure the downward trends in mortality rates would underestimate the premiums and reserves for annuity and pension products and then expose annuity and pension providers to the risks of financial distress. Since forecasting mortality rates accurately for a long period is extremely difficult, annuity and pension providers need to hedge the longevity risk by adopting some strategies and/or buying appropriate mortality-linked securities. Unlike interest-based securities which are widely created by financial researchers and traded in financial markets, mortality-linked securities have been rarely issued and traded. Facing the phenomenon of mortality improvement, annuity and pension providers now are in need of more mortality-linked securities as instruments for hedging longevity risk.The proposed research program pertains to modeling of mortality rates, hedging of longevity and mortality risks, and pricing of mortality-linked securities. In the project, I intend to focus on the following three main objectives:• For modeling of mortality, I would like to propose relational models (a relational model in modeling of mortality rates connects one mortality sequence to the other with some relationship) and its variations for in-sample mortality fitting and out-of-sample mortality forecasting; some important features including the cohort effect, a jump component, a common shock, dependency, stochastic processes and time series will also be involved in the models.• For hedging of mortality and longevity risks, I will apply my previously proposed mortality durations and convexities to a portfolio of three or more insurance products and to some other mortality-linked securities; the optimal problems regarding the weights producing the best performance of hedging mortality and longevity risks, respectively, will also be studied in details. • For pricing of existing mortality-linked securities based on the well-known Lee-Carter model or the proposed relational models, the features in the first objective will be considered to reflect one or more of various situations; new mortality-linked securities inspired from existing interest-based derivative ones will be proposed, and their pricing even though advanced financial mathematics is involved will be investigated to a great extent. The relational models and their variations are brand-new approaches to modeling mortality rates and hedging mortality/longevity risks. They are easy to implement, have good performance in mortality fitting/forecasting, and offer many potential applications due to their simplicity and effectiveness plus a relationship between two mortality sequences. The completion of this research program will help life insurers, social security and retirement benefit providers, and relevant industries reduce the possibilities of financial distress caused by mortality/longevity risks. I expect to make significant contributions to the field of mortality study.