Copula theory: an application to risk modeling

This paper compiles the research and experiments I carried out during my research project, as part of my penultimate year of engineering studies at Grenoble INP Ensimag. In this paper, we will present elements of the copula theory, including dependence coefficients in order to study copula properties on several examples. Then we will focus on risk management applications of copulas and particularly, the Loss Distribution Approach (LDA model). The model will be introduced as originally formulated in the context of operational risk and Basel II regulation. We will discuss the need for dependence modeling and comment the choice among several copulas, based on theoretical intuitions. Finally, we will take the LDA model into practice in the field of environmental risk. The experiment includes a full review of the advantages and drawbacks of the model. My research work was tutored by Stéphane Girard, an experienced research scientist at INRIA Rhône-Alpes. His expertise and research interests include statistics of the extremes, multivariate data analysis, functional estimation and applications of statistics. I was hosted by the Mistis team which is a joint venture between INRIA and Jean Kuntzman Laboratory in Grenoble. The activity of the team is focused on developing statistical methods in order to study and model complex random systems. The principle fields of application are image processing, spatial data, biomedical engineering and industry. I would like to thank warmly Stéphane Girard for his time, his insightful views on the subject and his tutoring all along the research project.