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We introduce a multivariate Poisson-Generalized Inverse Gaussian regression model with varying dispersion and shape for modeling different types of claims and their associated counts in nonlife insurance. The multivariate Poisson-Generalized Inverse Gaussian regression model is a general class of models which, under the approach adopted herein, allows us to account for overdispersion and positive correlation between the claim count responses in a flexible manner. For expository purposes, we consider the bivariate Poisson-Generalized Inverse Gaussian with regression structures on the mean, dispersion, and shape parameters. The model's implementation is demonstrated by using bodily injury and property damage claim count data from a European motor insurer. The parameters of the model are estimated via the Expectation-Maximization algorithm which is computationally tractable and is shown to have a satisfactory performance.

We introduce a random forest approach to enable spreads’ prediction in the primary catastrophe bond market. In a purely predictive framework, we assess the importance of catastrophe spread predictors using permutation and minimal depth methods. The whole population of non-life catastrophe bonds issued from December 2009 to May 2018 is used. We find that random forest has at least as good prediction performance as our benchmark-linear regression in the temporal context, and better prediction performance in the non-temporal one. Random forest also performs better than the benchmark when multiple predictors are excluded in accordance with the importance rankings or at random, which indicates that random forest extracts information from existing predictors more effectively and captures interactions better without the need to specify them. The results of random forest, in terms of prediction accuracy and the minimal depth importance are stable. There is only a small divergence between the drivers of catastrophe bond spread in the predictive versus explanatory framework. We believe that the usage of random forest can speed up investment decisions in the catastrophe bond industry both for would-be issuers and investors.

The key purpose of this paper is to present an alternative viewpoint for combining expert opinions based on finite mixture models. Moreover, we consider that the components of the mixture are not necessarily assumed to be from the same parametric family. This approach can enable the agent to make informed decisions about the uncertain quantity of interest in a flexible manner that accounts for multiple sources of heterogeneity involved in the opinions expressed by the experts in terms of the parametric family, the parameters of each component density, and also the mixing weights. Finally, the proposed models are employed for numerically computing quantile-based risk measures in a collective decision-making context.