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This paper is concerned with modelling multiple claim arrays that are subjectto one or more common shocks. It uses a structure that involves very generalforms both idiosyncratic and common shock components of cell means. Thedependencies between arrays, or between cells within an array, generated by theshocks are also of very general form. All of this appears in the priorliterature, where the idiosyncratic and shock components are additive. This hascreated the awkwardness of unbalanced shocks. The present paper rectifies thisby defining these components as multiplicative. Observations in individualscells of claim arrays are assumed log normal (later log Tweedie) in order toaccommodate the multiplicativity. Conveniently, the log normal case reducedparameter estimation to linear regression, yielding closed form solution oflocation parameters, and even of dispersion parameters in some cases.

Log normal claim models with common shocks