Mixtures of GLMs and number of components: application to surrender risk in life insurance.

Summary The issue of surrender has long been of concern to insurers, particularly in the context of life insurance savings contracts, for which colossal sums are at stake. The emergence of the European Solvency II directive, which recommends the development of internal models (of which an entire module is dedicated to the management of surrender behavior risks), reinforces the need to deepen our knowledge and understanding of this risk. It is in this context that we address in this thesis the issues of segmentation and modeling of surrenders, with the objective of better understanding and taking into account all the key factors that influence policyholders' decisions. The heterogeneity of behaviors and their correlation, as well as the environment to which policyholders are subjected, are as many difficulties to be treated in a specific way in order to make forecasts. We have developed a methodology that has produced very encouraging results and has the advantage of being replicable by adapting it to the specificities of different product lines. Through this modeling, model selection appears as a central point. We address it by establishing the strong convergence properties of a new estimator, as well as the consistency of a new selection criterion in the context of mixtures of generalized linear models.