Dependence Structures and Risk Aggregation Using Copulas

Insurance and reinsurance companies have to calculate solvency capital requirements in order to ensure that they can meet their future obligations to policyholders and beneficiaries. The solvency capital requirement is a risk management tool essential when extreme catastrophic events happen, resulting in high number of possibly interdependent claims. In this thesis, we study the problem of aggregating the risks coming from several insurance lines of business and analyse the effect of reinsurance in the level of risk. Our starting point is to use a Hierarchical Risk Aggregation method, which was initially based on 2-dimensional elliptical copulas. We use copulas from the Archimedean family and a mixture of different copulas. The results show that a mixture of copulas can provide a better fit to the data than the plain (single) copulas and consequently avoid overestimation or underestimation of the capital requirement of an insurance company. We also investigate the significance of reinsurance in reducing the insurance company's business risk and its effect on diversification. The results show that reinsurance does not always reduce the level of risk but can reduce the effect of diversification for insurance companies with multiple business lines. To extend the literature on modelling multivariate distributions, we investigate the dependence structure of multiple insurance business lines risks using C-vine copulas. In particular, we use bivariate copulas, and aggregate the insurance risks. We employ three C-vine models such as mixed C-vine, C-vine Gaussian and C-vine t-copula to develop a new capital requirement model for insurance companies. Our findings suggest that the mixed C-vine copula is the best model which allows a variety of dependence structure estimated by its respective copula families.