Future mortality rates are uncertain and the risk that estimated mortality rates will be higher than observed rates has negative financial implications for providers of living benefits including life annuities and pensions. This thesis studies time trends and cohort trends in mortality rates to determine the number of factors that drive mortality changes. An econometric analysis of mortality improvements is used to give a clearer picture of the stochastic nature of mortality rates in a lower dimensional data space as this thesis uses cointegration analysis for dimension reduction. A multi-country analysis of standardized mortality rates finds evidence of stochastic trends and a significant number of common factors. However, no evidence of common stochastic trends is found. An analysis of Australian mortality rates establishes there are non-stationary and stationary mortality rates by age. The common stochastic trends across age-groups which are exhibited within the Australian data lead to the characterization of mortality rates using a stochastic trend model. Dimension reduction is performed using the Heligman and Pollard (1980) parametric mortality model. The trends in the data are reflected using flexible Vector Autoregressive (VAR) models allowing for correlation between the estimated Heligman and Pollard model parameters. Bayesian Vector Autoregressive (BVAR) models which additionally quantify parameter risk are shown to significantly improve the forecast accuracy when fitting the developed HP-BVAR model to data from 1946-1995 and then comparing its out-of-sample forecasts to observed data from 1996-2007 for Australian mortality rates. Allowing for parameter uncertainty shows it to be a significant component of total risk since the results are realistic probabilistic forecasts. The HP-BVAR model is applied to the calibration of the longevity stress margin of the life insurance capital charge. The structure and magnitude of the current simplification by APRA result in a longevity stress margin that is found to be too prudent and too generalised. An alternative age-dependent simplification is proposed.