The life expectancy in industrialized countries has increased remarkably in recent decades. While most individuals consider this as a positive development, increased life expectancy has huge implications for governments, pension funds and insurancecompanies. Therefore actuaries and demographers make use of mortality models to forecast future mortality. Furthermore, the upcoming Solvency II regulations, which are due by 2013, require European insurance companies to quantify the uncertainty around the forecast of future mortality, i.e. mortality risk. Uncertainty quantification requires the need of models with stochastic features.Since its introduction in 1992 the Lee-Carter model has become the leading stochastic mortality model in the actuarial and demographic literature. Subsequently many extensions to the standard Lee-Carter model have been proposed. This thesis studies in particular the extension of the Lee-Carter model to the Poisson-gamma setting. Incomparison with the commonly used Poisson approach, the Poisson-gamma approach can explicitly capture unexplained variability in the data by introducing dispersion parameters. This thesis compares the two approaches using Dutch population mortality data.Insurance companies and pension funds do not face mortality risk related to a population, but mortality risk related to their portfolio. However, most stochastic mortality models cannot be fit reliably for portfolio mortality, because the amount of historical portfolio data is limited in terms of the size of the dataset as well as the number of years of portfolio data. In this thesis, we propose an extension to the Poisson-gamma Lee-Carter model for portfolio mortality estimation. The proposed extension applies Bayesian inference techniques based on the conjugacy of the Poisson and gammadistributions. Additionally, the proposed extension allows using the full forecasting ability of the Lee-Carter model. The mathematics behind the extension is closely related to credibility theory more commonly applied in the field of non-life insurance. We illustrate the results using the Dutch life and pension portfolio of the insurance company AEGON.