  In general insurance, risks from different categories are often modeled
independently and their sum is regarded as the total risk the insurer takes on
in exchange for a premium. The dependence from multiple risks is generally
neglected even when correlation could exist, for example a single car accident
may result in claims from multiple risk categories. It is desirable to take the
covariance of different categories into consideration in modeling in order to
better predict future claims and hence allow greater accuracy in ratemaking. In
this work multivariate severity models are investigated using mixture of
experts models with bivariate gamma distributions, where the dependence
structure is modeled directly using a GLM framework, and covariates can be
placed in both gating and expert networks. Furthermore, parsimonious
parameterisations are considered, which leads to a family of bivariate gamma
mixture of experts models. It can be viewed as a model-based clustering
approach that clusters policyholders into sub-groups with different
dependencies, and the parameters of the mixture models are dependent on the
covariates. Clustering is shown to be important in separating the data into
sub-groupings where strong dependence is often present, even if the overall
data set exhibits only weak dependence. In doing so, the correlation within
different components features prominently in the model. It is shown that, by
applying to both simulated data and a real-world Irish GI insurer data set,
claim predictions can be improved.
