  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.
