Dependence modeling and risk aggregation in actuarial science

点击翻译按钮获取中文摘要

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. ***The long-term objective of my research program is to pursue my research on dependence modelling and risk aggregation within both one-period risk models and dynamic risk models. The realization of my research program will contribute to the development of risk modelling and to the global risk assessment under dependence assumptions.***In the forthcoming years, I will first focus on the aggregation of dependent risks, the computation of the associated risk measures, and the derivation of the contribution under capital allocation rules, assuming the following contexts: (1) the joint distribution of the dependent risks is defined through a multivariate parametric distribution; (2) the joint distribution is defined by a multivariate Archimedean copula and its marginal univariate distributions; and (3) the joint distribution is partially specified. I will also focus on the computation of ruin measures and risk measures defined in terms of ruin probabilities within discrete-time and continuous-time dynamic risk models assuming a temporal dependence. ***My research program incorporates an HQP training plan which will provide my students with scientific rigor and a strong training in actuarial risk theory, dependence modeling, aggregation of dependent risks, and capital allocation methods, which will help them either if they pursue an academic career or if they get a position in the actuarial practice, where the financial stakes can be substantial.