Negative binomial models for development triangles of counts

Prediction of outstanding claims has been done via nonparametric models (chain ladder), semiparametric models (overdispersed poisson) or fully parametric models. In this paper, we propose models based on negative binomial distributions for the prediction of outstanding number of claims, which are particularly useful to account for overdispersion. We first assume independence of random variables and introduce appropriate notation. Later, we generalise the model to account for dependence across development years. In both cases, the marginal distributions are negative binomials. We study the properties of the models and carry out bayesian inference. We illustrate the performance of the models with simulated and real datasets.