B1855
Title: Risk models defined on a family of tree-based Markov random fields with Poisson marginals
Authors: Etienne Marceau - Laval University (Canada) [presenting]
Abstract: A new family of tree-based Markov random fields for a vector of discrete counting random variables are presented. According to the characteristics of the family, the univariate distribution of the random variables is Poisson and the structure of dependence between them is encrypted in a tree. This new family is used as a basis for building multivariate collective risk models, which makes it possible to integrate the flexibility specific to graphic models into actuarial modeling. That approach allows building a family of multivariate compound Poisson distributions that can be appropriate in the context of high-dimensional portfolios of non-life insurance contacts. The proposed family of tree-based Markov random fields for a vector of discrete counting random variables has many advantages, notably developing computational methods, such as sampling. For example, thanks to the specific properties of the new family, the joint probability-generating function is identified as the vector of counting random variables. That result allows for finding the distribution of the aggregate claim random variable of the entire portfolio. The computational methods scale well to portfolios of high dimensions. Estimation and calibration procedures are also discussed.
