Bayesian analysis of compound loss distributions

Bayesian analysis is performed to scrutinize the compound loss distribution using sampling based methods. Both the number and the size of the losses are treated in a stochastic manner. Model selection, forecasting and reinsurance are studied from the predictive distribution. Model uncertainty is incorporated in forecasting through the use of posterior probabilities. The variation of the aggregate claim amount is analyzed under different reinsurance treaties. The methodology for modeling collective distributions of insurance losses is illustrated by an example.