Analysis of New Techniques for Risk Aggregation and Dependence Modelling

In risk aggregation we are interested in the distribution of the sum of dependent risks. The objective of risk aggregation and dependence modeling is to model adequately dependent insurance portfolios in order to evaluate the overall risk exposure. This master thesis investigates some practical aspects of modeling risk aggregation and dependency. We give an introduction to copula-based hierarchical aggregation model through reordering algorithm. This approach can be easily applicable in high dimensions and consists of a tree structure, bivariate copulas, and marginal distributions. This method is empirically illustrated using data set of Danish Fire Insurance Data. These data were collected at Copenhagen Reinsurance over the period 1980 to 1990 and every total claim has been divided into three risks consisting of a building loss, a loss of contents and a loss of profits caused by the same fire.