Portfolio Claims Reserving with Univariate and Multivariate Generalized Link Ratios

Correlations between claims in insurers’ lines of business may change results obtained on claims reserving. Here, we develop univariate and multivariate generalized link ratios for use with portfolio data, that is, estimating several triangles at the same time with correspondent correlations. Two options are presented, with the univariate case just considering correlations between triangles and not inside each triangle, and the multivariate case considering correlations between triangles and inside each triangle. Due to this extension, we call these methods as from portfolio data, because they consider more than one triangle at the same time. Existence/no-existence of correlations inside each triangle is called a multivariate/univariate approach with portfolio data. We also show that, from these methods, we may extract several others with different ways of estimating loss development factors. It is the case of heteroscedastic methods as chain ladder and simple average and homoscedastic ones as vector projection. Other heteroscedastic methods are also extracted with different levels of heteroscedasticity as the ones obtained for chain ladder and simple average. Some numerical examples, with standard data, are presented, and they confirm the use of vector projection as the solution that minimizes the prediction error, both for univariate and multivariate cases, and when using portfolio data.