Actuarial risk models with dependence

点击翻译按钮获取中文摘要

For an insurance company or an investment firm, it is of utmost importance to make an adequate assessment of the global risk of a portfolio which can be 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. 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 must still be accomplished in this young research field in order to have adequate models and tools that allow a good understanding of the global risk of a portfolio. With my research program, I will contribute to the development of short term and long term risk modelling and global risk assessment under dependence assumptions. More precisely, I will derive aggregation methods, analyze risk measures and capital allocation within portfolios with dependent risks. I will also analyze risk and ruin measures within three types of continuous-time risk models: earthquake models, risk models with general dependence structure between interclaim times and losses, and dependent Sparre-Andersen risk models with interest. Finally, I will analyze risk and ruin measures within discrete-time risk models with three different forms of dependence structure: temporal dependence, random income, and correlated classes of business.