Univariate and multivariate claims reserving with Generalized Link Ratios

In actuarial practice, it is important to select an adequate claims reserving method for each line of business, however it might not always be appropriate to apply the same method for all triangles involved in the portfolio of business. In this regard, we develop a versatile univariate and multivariate Generalized Link Ratios framework, inside the same triangle, that includes some existing methods (such as the chain-ladder, vector projection, and simple average) as special cases, and calculates the prediction errors analytically. Our methodology allows us to simultaneously estimate the loss development factors, the reserves, and the prediction errors over all the regressions, without utilizing recursive formulas. Further, the criterion employed for the model selection, which is based on the lowest prediction error, also estimates a key parameter that corresponds to a certain level of heteroscedasticity. Finally, several numerical examples with irregular, regular, and real data illustrate the applicability of our treatment and check the assumptions made in the paper.