| Summary: | In most developed economies, the insurance sector earns premiums that amount to around eight percent of their GNP. In order to protect both the financial market and the real economy, this results in strict regulations, such as the Solvency II Directive, which has monitored the EU insurance sector since early 2016. The largest item on general insurers’ balance sheets is often liabilities, which consist of future costs for reported claims that have not yet been settled, as well as incurred claims that have not yet been reported. The best estimate of these liabilities, the so-called reserve, is given attention to in Article 77 of the Solvency II Directive. However, the guidelines in this article are quite vague, so it is not surprising that modern statistics has not been used to a great extent in the reserving departments of insurance companies. This thesis aims to combine some theoretical results with the practical world of claims reserving. All results are motivated by the chain ladder method, and provide different reserving methods that will be introduced thoughout four separate papers. The first two papers show how claim estimates can be embedded into a full statistical reserving model based on the double chain ladder method. The new methods introduced incorporate available incurred data into the outstanding liability cash flow model. In the third paper a new Bornhuetter-Ferguson method is suggested, that enables the actuary to adjust the relative ultimates. Adjusted cash flow estimates are obtained as constrained maximum likelihood estimates. The last paper addresses how to consider reserving issues when there is excess-of loss reinsurance. It provides a practical example as well as an alternative approach using recent developments in stochastic claims reserving.
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