Trend analysis and prediction procedures for time nonhomogeneous claim processes

The paper focuses on time nonhomogeneous claim occurrence processes. Such processes arise either in a natural way, as a result of modelling (often qualitative-type) assumptions, or when a trend may exist and needs to be allowed for in the model construction. For trend analysis, we use trend representations which are formulated on the basis of an appropriate process characteristic in conjunction with a probabilistic ordering notion. Such trend representations are verified for a given process with respect to assumptions on its stochastic behaviour. Making predictions with regard to quantities of interest such as the time to the next claim or the expected total number of claims in the next year is the other major goal of this work. The predictions are obtained by employing Bayesian revision procedures for different inference models on the claim occurrence process.