This paper is concerned with modelling multiple claim arrays that are subject to one or more common shocks. It uses a structure that involves very general forms both idiosyncratic and common shock components of cell means. The dependencies between arrays, or between cells within an array, generated by the shocks are also of very general form. All of this appears in the prior literature, where the idiosyncratic and shock components are additive. This has created the awkwardness of unbalanced shocks. The present paper rectifies this by defining these components as multiplicative. Observations in individuals cells of claim arrays are assumed log normal (later log Tweedie) in order to accommodate the multiplicativity. Conveniently, the log normal case reduced parameter estimation to linear regression, yielding closed form solution of location parameters, and even of dispersion parameters in some cases.
翻译:本文涉及建模受到一种或多种常见冲击的多重索赔阵列,它使用一种结构,涉及非常一般的形式,既包括单元格手段的特异和常见冲击元件。由冲击产生的阵列之间或阵列内的细胞之间的依赖性也是非常一般的形式。所有这一切都出现在以前的文献中,其中的特异和冲击元件是添加的。这造成了不平衡冲击的尴尬性。本文件通过将这些组成部分定义为倍增性来纠正这一点。为了适应倍增性,对个别索赔阵列的观察假定为日志正常(后日志 Tweedie ) 。逻辑普通案例将参数估计降低到线性回归,从而得出了定位参数的封闭形式解决方案,在某些情况下甚至得出了分散参数。