  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.
