The paid-incurred chain (PIC) reserving method is a claims reserving method that allows to combine claims payments and incurred losses information in a mathematical consistent way. The main criticism on the original Bayesian log-normal PIC model presented in Merz–Wüthrich [5] is that it does not respect dependence properties within the observed data. In the present paper, we extend the original Bayesian log-normal PIC model so that dependence is modeled in an appropriate way.

We use economic indicators to improve the prediction of the number of incurred but not recorded disability insurance claims, assuming that there is a link between the number of claims and the chosen economic indicators. We propose a Bayesian model where we model the claims development in three directions: along incurred periods, recording lag periods and calendar periods. A stochastic model of the economic indicators is incorporated into the calendar period development direction. Thus we allow for the impact of the economic environment on the number of claims. Applying the proposed model to data, we illustrate how the inclusion of economic indicators affects the prediction of the number of incurred but not recorded disability claims.

We consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. We choose two different types of prior distributions for the parameters and then study the different Bayesian predictors. This study leads, on the one hand, to the classical chain ladder predictor and, on the other hand, to Bornhuetter & Ferguson predictors. We highlight (either analytically or numerically) how these predictors are obtained and how their prediction uncertainty can be determined.