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For life insurance and annuity products whose payoffs depend on the future mortality rates, there is a risk that realized mortality rates will be different from the anticipated rates accounted for in their pricing and reserving calculations. This is termed as mortality risk. Since mortality risk is difficult to diversify and has significant financial impacts on insurance policies and pension plans, it is now a well-accepted fact that stochastic approaches shall be adopted to model the mortality risk and to evaluate the mortality-linked securities. The objective of this thesis is to propose the use of a time-changed Markov process to describe stochastic mortality dynamics for pricing and risk management purposes. Analytical and empirical properties of this dynamics have been investigated using a matrix-analytic methodology. Applications of the proposed model in the evaluation of fair values for mortality linked securities have also been explored. To be more specific, we consider a finite-state Markov process with one absorbing state. This Markov process is related to an underlying aging mechanism and the survival time is viewed as the time until absorption. The resulting distribution for the survival time is a so-called phase-type distribution. This approach is different from the traditional curve fitting mortality models in the sense that the survival probabilities are now linked with an underlying Markov aging process. Markov mathematical and phase-type distribution theories therefore provide us a flexible and tractable framework to model the mortality dynamics. And the time-changed Markov process allows us to incorporate the uncertainties embedded in the future mortality evolution. The proposed model has been applied to price the EIB/BNP Longevity Bonds and other mortality derivatives under the independent assumption of interest rate and mortality rate. A calibrating method for the model is suggested so that it can utilize both the market price information involving the relevant mortality risk and the latest mortality projection. The proposed model has also been fitted to various type of population mortality data for empirical study. The fitting results show that our model can interpret the stylized mortality patterns very well.