9.1 Motivation for Flexible Parametric Severity Loss Models
In Chapter 5, we provided a description of standard loss distribution models. In the case of severity models, this has included LogNormal, Gamma, Weibull, Pareto, and Generalized Pareto models. In the case of frequency-based models, the families of Poisson, Binomial, and Negative Binomial have been considered. In this chapter, we provide a more flexible set of models that should be considered by OpRisk practitioners, especially in the modeling of heavytailed loss processes.
In the following subsections, we will first introduce important members of the general family of heavy-tailed loss models for the severity distribution; some of these will also be members of the subexponential family of models or models with different properties of tail variation as well as flexible skew and kurtosis characteristics. It is typical when modeling such severity distributions to consider families of models that have members which take positive support and are typically unimodal and left skewed. The models presented in the following sections introduce several families of parametric statistical models that are of direct interest in the areas of OpRisk and insurance modeling. The focus will be on severity models under a Loss Distribution Approach (LDA) structure and the properties of the considered parametric families that make them amenable to heavy-tailed modeling in OpRisk.