General Reinsurance

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Summary

The paper is a survey on the author's research on the classical largest claims cover and modifications of it, done since the beginning of the eighties over about 20 years. It has the aim to inform the international actuaries on the results of that voluminous research project published in many papers in diverse actuarial journals. The main results are derived more general for a generalized treaty, called generalized largest claims reinsurance cover (short: GLCR). In the first, biggest part of the theory general results on the premium of the GLCR are derived. Four different approaches are considered, first the so-called direct method, second the so-called bounding method, third the so-called recursive method and fourth the so-called asymptotic method. The second part of the theory is dedicated to the total claims amount R that the reinsurer has under such a GLCR. With help of the concept of the so-called spacing general results on the distribution function of R and its density can be derived. At a further fourier-type method is pointed, by citing the relevant publication. In the last part of the theory one investigates with the efficiency of certain generalizations of the GLCR, that include also as special case the classical excess-of-loss treaty. As example e.g. the comparison of the classical largest claims and the excess-of-loss treaty is mentioned.

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