In the area of financial risk assessment and actuarial calculation it is important to know the probability for two or more risks to occur at the same time. We cannot assume these risks to be independent and thus have to find a way of modeling the dependence between two or more risk factors with known marginal behavior. In order to determine the joint distribution of the risk factors, we choose the copula approach, which enables us to isolate the description of the dependence structure. The copula approach does measure non-linear dependence. This thesis specifies the basic properties of copulas in general as well as the properties of Archimedean copulas. After defining Archimedean copulas, we will introduce the description of Archimedean copulas in terms of Laplace-Stieltjes transforms. The Laplace-Stieltjes approach then gives us an algorithm which allows us to sample from Archimedean copulas. Hence, well-known Archimedean copula families are introduced and algorithms are given, which enable us to sample from them. In the case of the Clayton copula family, the algorithm is implemented in MATLAB. Finally, an overview of dependence measures derived from copulas is given and special properties of dependence measures derived from Archimedean copulas are emphasized.     «

In the area of financial risk assessment and actuarial calculation it is important to know the probability for two or more risks to occur at the same time. We cannot assume these risks to be independent and thus have to find a way of modeling the dependence between two or more risk factors with known marginal behavior. In order to determine the joint distribution of the risk factors, we choose the copula approach, which enables us to isolate the description of the dependence structure. The copul...     »