Dependence modeling and risk aggregation in actuarial science

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In recent years, it has become crucial for insurers and financial institutions to develop efficient risk management tools to have an appropriate assessment of the global risk associated to a portfolio which may consist of a group of insurance policies, different lines of business or different risks of an investment institution. A fair quantification of this risk must be done to insure the company’s solvability. Risk theory in actuarial science aims to measure adequately this global risk, which can be examined with one-period risk models, defined over a fixed period of time. It can also be assessed with dynamic risk models by examining the behavior of the portfolio over several periods, either with discrete-time risk models or continuous-time risk models. The classical risk models propose to assess the global risk under assumptions of independence between risks and/or through time. These assumptions often lead to an inappropriate assessment of the global risk faced by insurers or investment firms. In recent years, more complex risk models which account for these dependence relations have been proposed and studied. However, much work remains to be done in this research field in order to have adequate models and tools that allow a good understanding of the global risk of a portfolio. During my last granting period, most of my research has been devoted to dependence modelling and risk aggregation within both one-period risk models and dynamic risk models.