Multivariate loss prediction in the multivariate additive model

In the present paper we propose a multivariate version of the additive model of loss reserving. The multivariate additive model is a linear model with a particular design matrix and a particular variance structure and is suitable for certain portfolios consisting of several correlated subportfolios. Under the assumptions of the multivariate additive model, we derive a formula for the Gauss-Markov predictor for a non-observable incremental claim. We also show that the Gauss-Markov predictors for the reserve of a particular accident year and for the total reserve are obtained by summation over the Gauss-Markov predictors for the corresponding non-observable incremental claims, and that this is also true for the Gauss-Markov predictors for the corresponding quantities of the aggregate portfolio.