The increase in the use of copulas has introduced implementation issues for both practitioners and researchers. One of the issues is to obtain a copula function for a given set of data. The most common approaches for the estimation of the parameters of the copula functions have been the Maximum Likelihood Estimator (MLE) and the Inference Functions for Margins (IFM) methods. Archimedean copulas are one of the most important classes of copulas that are widely used in both finance and insurance for modelling dependent risks. However, simulating multivariate Archimedean copulas has always been a difficult task as the number of dimensions increases. The assessment of capital requirements has always been an important application of stochastic modelling. Capital requirements can vary significantly depending on the model adopted. Several professional bodies have recently discussed the concept of dependencies between insurance risks. They suggest that insurers should use a technique based on copulas to describe the dependence of risks within an insurance company in the context of solvency assessment. The first contribution of this thesis is to provide an insight into the efficiency of parameter estimation methods. This thesis uses numerical experiments to assess the performance of the two common approaches. The second contribution of this thesis is to present a new algorithm to simulate multivariate Exchangeable Archimedean copulas. This algorithm provides a practical solution for simulating one-parameter multivariate Archimedean copulas. Numerical experiments are used to apply this algorithm to determine the "additional" economic capital for an insurance company with multiple lines of business that wants to expand its business by adding another line of business and where the businesses are dependent. The third contribution of this thesis is to quantify the impact of the choice of copulas on the solvency measure of a general insurer within a Dynamic Financial Analysis modelling framework. The results of our experiments provide important guidance for the capital assessment for general insurers.
| Identifer | oai:union.ndltd.org:ADTP/257610 |
| Date | January 2007 |
| Creators | Wu, Mei Lan, Actuarial Studies, Australian School of Business, UNSW |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://unsworks.unsw.edu.au/copyright, http://unsworks.unsw.edu.au/copyright |
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