The paper is concerned with common shock models of claim triangles. These are usually constructed as a linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses 'auto-balanced' models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.
翻译：本文涉及索赔三角形的常见冲击模型,这些模型通常是由冲击元件和独特元件组成的线性组合。以前的文献讨论了这些模型的不平衡特性,根据这些特性,冲击可能会过度或不足地促成某些观察。文献还提出了这方面的更正。本文件讨论了“自动平衡”模型,其中所有冲击元件和独特元件都有助于观察,因此,它们从观察到不同观察,其比例贡献是稳定的。自动平衡的条件被认为简单,适用于广泛的模型结构。提供了数字说明。
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