Stochastic Mortality Modelling

For life insurance and annuity products whose payoffs depend on the future mortality rates, there is a risk that realizedmortality rates will be different from the anticipated ratesaccounted for in their pricing and reserving calculations. This istermed as mortality risk. Since mortality risk is difficult todiversify and has significant financial impacts on insurancepolicies and pension plans, it is now a well-accepted fact thatstochastic approaches shall be adopted to model the mortality riskand to evaluate the mortality-linked securities.The objective of this thesis is to propose the use of atime-changed Markov process to describe stochastic mortalitydynamics for pricing and risk management purposes. Analytical andempirical properties of this dynamics have been investigated usinga matrix-analytic methodology. Applications of the proposed modelin the evaluation of fair values for mortality linked securitieshave also been explored.To be more specific, we consider a finite-state Markov processwith one absorbing state. This Markov process is related to anunderlying aging mechanism and the survival time is viewed as thetime until absorption. The resulting distribution for the survivaltime is a so-called phase-type distribution. This approach isdifferent from the traditional curve fitting mortality models inthe sense that the survival probabilities are now linked with anunderlying Markov aging process. Markov mathematical andphase-type distribution theories therefore provide us a flexibleand tractable framework to model the mortality dynamics. And thetime-changed Markov process allows us to incorporate theuncertainties embedded in the future mortality evolution.The proposed model has been applied to price the EIB/BNP LongevityBonds and other mortality derivatives under the independentassumption of interest rate and mortality rate. A calibratingmethod for the model is suggested so that it can utilize both themarket price information involving the relevant mortality risk andthe latest mortality projection. The proposed model has also beenfitted to various type of population mortality data for empiricalstudy. The fitting results show that our model can interpret thestylized mortality patterns very well.