Contributions of Statistical Learning to Actuarial and Financial Risk Management.

Summary The continuous increase in computer performance over the past decades has allowed for the widespread application of statistical learning theory in many fields. In particular, actuaries, historical experts in statistics, are increasingly turning to these innovative algorithms for the assessment of the risks they face. Thus, in this thesis, we examine how the integration of methodologies from statistical learning can contribute to the development of actuarial sciences and risk management through the study of three independent problems, presented in a general introduction. The first two chapters propose new mortality projection models in the context of the evaluation of longevity risk carried by insurance companies or pension funds. Chapter 1 focuses on the case where a single population is studied, while Chapter 2 extends the analysis to multi-populations. In both situations, the problem of high dimensionality appears central and we address it using a penalized vector autoregression (VAR). This model is applied directly on the mortality improvement rates in the first chapter, and on the time series resulting from the estimation of a Lee-Carter model for the second. The elastic-net penalty allows us to keep the great freedom of the space-time dependence structure offered by the VAR while remaining parsimonious in the number of parameters, and thus avoid overlearning. In Chapter 3 we analyze the surrender risk of life insurance contracts using supervised classification algorithms. Among others, we apply the wide margin separator (SVM) and the extreme gradient boosting (XGBoost). In order to compare the performances of the different classifiers, we adopt an economic vision from the marketing literature based on the potential profits of a retention campaign. We insist on the importance of the loss function retained in the statistical learning algorithms according to the objective sought: the use of a loss function in connection with the performance measure brings a significant improvement in the application of the XGBoost in our study. Finally, in the context of financial risk management, we study the dynamics of agricultural prices during particular trading sessions where government reports, containing valuable information for agents, are published. We examine the potential of open access data, in particular satellite images of vegetation index made available by NASA, for predicting market reactions. We then propose avenues of improvement to consider for practical implementation of this data enrichment methodology in risk management.