Dependence Structures and Limiting Results

"Extreme, synchronized rises and falls in financial markets occur infrequently but they do occur. The problem with the models is that they did not assign a high enough chance of occurrence to the scenario in which many things go wrong at the same time - the em perfect storm scenario" (Business Week, September 1998). This book focuses on limiting theorems for copulae. Because joint dependences of extremal events is nowadays is key issue in risk management, it becomes crucial to get a better understanding of behavior of copulas in tails. The first chapter presents a survey on copulae, and possible applications in risk management. The following chapters present some canonical theorems for copulae, and the link between this approach and standard results on multivariate extreme is explained. A concluding chapter presents a survey on graphical procedures to represent copula densities (with proper fit) in tails.