Risk models with dependence in actuarial science/ Modèles de risque avec dépendance en sciences actuarielles

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An appropriate assessment of the global risk of a portfolio is crucial for an insurance company or an investment firm. In actuarial science, the main objective of risk theory is to evaluate this global risk. The latter can be examined with short term risk models over a fixed period of time. It can also be assessed with long term dynamic risk models by examining the behaviour of the portfolio over several periods, either with discrete-time risk models or continuous-time risk models. It is clear that risk models traditionally based on the independence assumption underestimate or overestimate the global risk. Better, more complex models are needed to account for dependence among risks and/or through time. These improvements require new approaches and methods to quantify appropriately the global risk. During the last six years, most of my research has been devoted to short term risk models, continuous-time risk models and discrete-time risk models with dependence. My present and long-term objective is to pursue the study of risk models with dependence in actuarial science. The short-term objectives are: (1) To propose dependence structures in short term risk models, to develop aggregation methods in order to evaluate risk measures within the proposed models and to determine the capital allocation; (2) To propose continuous-time and discrete-time risk models with dependence, to evaluate ruin measures, and to evaluate the risk quantities (such as the discounted aggregate claim amount) in discrete-time and continuous-time risk models with dependence. In the long run, the realization of my research program will provide new tools to actuaries, enabling them to measure and qualify the global risk of a portfolio of risks under the assumption of possible dependence.