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.

翻译：未决索赔的预测通常通过非参数模型（链梯法）、半参数模型（过离散泊松模型）或完全参数模型实现。本文提出基于负二项分布的模型用于预测未决索赔次数，该模型特别适用于处理过离散现象。我们首先假设随机变量相互独立并引入相应符号体系，随后将模型推广至考虑不同进展年间的相依性。两种情形下的边际分布均为负二项分布。我们研究了模型的性质并执行贝叶斯推断，通过模拟数据集与真实数据集验证了模型的性能。