Contribution to the study of prevention in health insurance.

Summary This thesis deals with the implementation of prevention actions financed by an insurance company. It is composed of five chapters preceded by a general introduction which aims to present the difficulties linked to prevention, the tools used and the main results obtained. Chapter 1 proposes a method of unsupervised classification of health insurance policyholders into homogeneous risk groups, based on the benefits paid by an insurance company. This method has two phases: first, a dimension reduction of the data using positive matrix factorizations (PMF) is performed. The classification is then finalized using Kohonen maps. The tests of the method are also presented. The final classes obtained are finally analyzed in order to study whether some of them can be the object of a prevention action. A prevention action on psychiatry is proposed. Chapter 2 is a continuation of Chapter 1 since it focuses on comparing the quality of dimension reduction using NMF methods with that obtained using two other methods, the Word2Vec (W2V) and the marginalized stacked debugger autoencoders (mSDA). In particular, the stability of the final classifications is studied using a new stability measure. A complement on the consideration of temporality with the W2V algorithm is also presented. Chapter 3 proposes a study of the psychiatric risk within a complementary health organization, the algorithms of the previous chapters having allowed to identify this risk. With the help of a statistical study conducted on four databases, it is notably shown that insureds using psychiatry cost on average twice as much to the health insurer as an average individual. Some potential preventive actions are suggested in the conclusion. Chapter 4 focuses on the modelling of prevention within an insurance company. By integrating a prevention parameter into the compound Poisson model derived from the theory of ruin, it is indeed possible to measure the effect of prevention on certain indicators, such as the probability of ruin. Different optimal prevention strategies are proposed, and a sensitivity analysis is provided. Finally, chapter 5 proposes to extend the model considered in the previous chapter to the case where an insurance company is confronted with a light risk and a heavy risk. In such a model, the optimal prevention strategy depends on the amounts of reserves built up. Asymptotic results on the optimal strategies are provided.