Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, complications arise in the presence of “unbalanced data”, that is, when (expected) magnitude of observations over a single triangle, or between triangles, can vary substantially. Specifically, if a single common shock is applied to all of these cells, it can contribute insignificantly to the larger values and/or swamp the smaller ones, unless careful adjustments are made. This problem is further complicated in applications involving negative claim amounts. In this paper, we address this problem in the loss reserving context using a common shock Tweedie approach for unbalanced data. We show that the solution not only provides a much better balance of the common shock proportions relative to the unbalanced data, but it is also parsimonious. Finally, the common shock Tweedie model also provides distributional tractability.

中文翻译：

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随机损失准备金中的不平衡数据和常见冲击模型

引入共同冲击是一种流行的依赖建模方法，最近在损失准备金中有一些应用。这种方法的主要优点是能够捕获来自已知关系的结构依赖性。此外，它有助于简化大维相关矩阵的构造。然而，在存在“不平衡数据”的情况下会出现复杂情况，也就是说，当单个三角形上或三角形之间的（预期）观测值可能有很大差异时。具体来说，如果对所有这些单元施加一个共同的冲击，它可能对较大的值贡献微不足道和/或淹没较小的值，除非进行仔细调整。这个问题在涉及负索赔额的申请中更加复杂。在本文中，我们在损失保留上下文中解决了这个问题，对不平衡数据使用了一种常见的冲击 Tweedie 方法。我们表明，该解决方案不仅提供了相对于不平衡数据更好的常见冲击比例平衡，而且它也是简约的。最后，常见的Shock Tweedie 模型还提供了分布易处理性。