In this thesis, we apply three Bayesian econometric tools in the area of longevity risk management. Firstly, we develop an algorithm to Mortality modelling under the Bayesian state-space framework. Our framework allows for efficient and fast estimation of model parameters. Secondly, we provide a new hypothesis testing method using Bayesian Decision Theory applied in annuity liabilities, which is a more robust approach to the standard Null Hypothesis Significance Testing. Lastly, we provide a Bayesian risk premium analysis for longevity derivatives.