Covariance extension of Chain-ladder method

This diploma thesis deals with technical reserves in non-life insurance, in particular with provisions for future claim payments for damages that have occurred, but has not yet been reported to the insurance company. This type of provision is known by the acronym IBNR. After the introductory section containing a general introduction to the issue of claims reserving in non-life insurance different approaches to modeling of IBNR reserves are briefly presented. Subsequently, full attention is given to Chain-ladder method, which is most frequently used in the actuarial practise for the purpose of claims reserving. This method is then presented progressively from its simplest form of a simple computing algorithm followed by Mack's stochastic model to the last theoretical part of this part describing extended form of Chain-ladder method with relations between different groups of insurance portfolio included. In the very last section, all the lessons are demonstrated on real data to give readers an idea of how the process of claims reserving works is in the common actuarial practice.