• Citer

On the measure of risks in a ruin context and the measure of dependence.

par Zuyderhoff, Pierre
Président du jury Verdebout, Thomas
Promoteur Trufin, Julien
Publication Non publié, 2021-09-03

Thèse de doctorat

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

For an insurance company, one of the main objectives in risk management is to assess the risk associated with an insurance portfolio. In insurance mathematics, ruin theory is a traditional tool for performing such an evaluation. In the context of this theory, the time evolution of the reserve of an insurance company is modelled by a long-term risk process. In order to assess the riskiness of such a process, an appropriate risk measure is needed. However, there is no single number that captures all the characteristics of the risk associated with the process. Hence, there is a need to develop multiple risk measures, and to select an appropriate risk measure depending on the context in mind. Another issue related to many risk management situations is the need to properly measure the dependency between two random variables. Standard dependence measures include Spearman rank correlation coefficient and Kendall rank correlation coefficient. In this context, the case where at least one of the random variables is discrete is qualitatively different from the continuous case. This situation occurs, for example, when one wishes to assess the dependence between the annual number of claims for policyholders who experienced at least one claim and the average claim severity. In this case, the results of dependency measures need to be interpreted differently since small values of these measures may actually support strong dependence. This thesis consists of two parts. The first part is devoted to ruin theory. Although ruin theory is the subject of abundant literature, questions remain unanswered. We aim to give answers to questions related to computation, properties and applications of ruin-based risk measures within both continuous and discrete-time models. In the second part, we derive bounds on Spearman's rho in case of at least one random variable is discrete. A motivation for this is given in terms of applications of practical relevance.