Bayesian analysis of claim run-off triangles

This dissertation studies Markov chain Monte Carlo (MCMC) methods, and applies them to actuarial data, with a focus on claim run-off triangles. After reviewing a classical model for run-off triangles proposed by Hertig (1985) and improved by de Jong (2004), who incorporated a correlation structure, a Bayesian analogue is developed to model an actuarial dataset, with a view to estimating the total outstanding claim liabilities (also known as the required reserve). MCMC methods are used to solve the Bayesian model, estimate its parameters, make predictions, and assess the model itself. The resulting estimate of reserve is compared to estimates obtained using other methods, such as the chain-ladder method, a Bayesian over-dispersed Poisson model, and the classical development correlation model of de Jong. The thesis demonstrates that the proposed Bayesian correlation model performs well for claim reserving purposes. This model yields similar results to its classical counterparts, with relatively conservative point estimates. It also gives a better idea of the uncertainties involved in the estimation procedure