A general multivariate chain ladder model

A general multivariate stochastic reserving model is formulated, which not only specifies contemporaneous correlations, but also allows structural connections among triangles. Its structure extends the existing multivariate chain ladder models in a natural way, and this extension proves to be advantageous in improving model adequacy and increasing model flexibility. It is general in the sense that it includes various models in the chain ladder framework as special cases. At the heart of this model is the seemingly unrelated regression technique, which is utilized to estimate parameters that reflect contemporaneous correlations. The use of this technique is essential to construct flexible models, and related statistical theories are applied to study properties of existing estimators. A numerical example is utilized to show the advantage of the proposed model in studying multiple triangles that are related both structurally and contemporaneously.