General Insurance Reserve Risk Modeling Based on Unaggregated Data

Recently the eld of actuarial mathematics has experienced a large development due to a signi cant increase of demands for insurance and nancial risk quanti cation due to the fact that the implementation of a complex of rules of international reporting standards (IFRS) and solvency reporting (Solvency II) has started. It appears that the key question for solvency measuring is determination of probability distribution of future cash ows of an insurance company. Solvency is then reported through an appropriate risk measure based e.g. on a percentile of this distribution. While as present popular models are based solely on aggregated data (such as total loss development from a certain time period), the main objective of this work is to scrutinize possibilities of modelling of the reserve risk (i.e. roughly said, the distribution of the ultimate incurred value of claims that have already happened in the past) based directly on individual claims. These models have not yet become popular and to the author's knowledge an overview of such models has not been published previously. The assumptions and speci cation of the already published models were compared to the practical experience and some inadequacies were pointed out. Further more a new reserve risk model was constructed which is believed to have practically more suitable assumptions and properties than the existing models. Theoretical aspects of the new model were studied and distribution of the ultimate incurred value (the modelled variable) was derived. An emphasis was put also on practical aspects of the developed model and its applicability in the case of industrial use. Therefore some restrictive assumptions which might be considered realistic in variety of practical cases and which lead to a signi cant simpli cation of the model were identi ed throughout the work. Furthermore, algorithms to reduce the number of the necessary calculations were developed. In the last chapters of the work, an e ort was devoted to the methods of the estimation of the considered parameters respecting practical limitations (such as missing observations at the time of modelling). For this purpose, survival analysis was (amongst other methods) applied.