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.

中文翻译：

---

一个 Gamma 移动平均过程，用于在径流三角形中对跨发展年的依赖性进行建模

我们提出了一个索赔准备金的随机模型，该模型在单个三角形内捕获了沿发展年份的依赖关系。这种相关性基于具有移动平均顺序的伽马过程$p \ge 0$这是通过使用泊松潜变量来实现的。我们对模型参数进行贝叶斯推理，并通过使用分层先验来跨多个三角形借用强度，这些三角形来自不同的业务线或公司。我们进行模拟研究以及真实数据分析。结果表明，对于所研究的真实数据集，与假设独立的基准过度分散泊松相比，我们的伽马依赖模型更准确。