We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

我们提出了一种用于索赔准备的随机模型，该模型捕获了单个三角形内沿开发年份的依赖性。这种依赖关系是基于伽马过程，其移动平均值形式为 $ p \ ge 0 $ ，这是通过使用泊松潜变量实现的。我们通过使用分层先验，对模型参数进行了贝叶斯推断，并跨越了来自不同行业或公司的多个三角形的借用强度。我们进行了模拟研究以及真实的数据分析。结果表明，与假设独立的基准过分散泊松相比，对于我们研究的真实数据集，储量估计值使用我们的伽马依赖性模型更为准确。