Simulations of Extreme Losses in Non-Life Insurance

The analyses of insurance risks are an important part of the project of Solvency II preparing of European Commission. The risk theory is the analysis of the stochastic features of non-life insurance business. The field of insurance risk theory has grown rapidly. There are now many papers and textbooks, which study the foundations of risk processes along strictly theoretical lines. On the other hand there is a need to develop the theories into forms suitable for practical purposes and to demonstrate their application. Modern computer simulation techniques open up a wide field of practical applications for risk theory concepts, without requiring the restrictive assumptions and sophisticated mathematics, of many traditional aspect of insurance risk theory.. Modelling the size or loss is of crucial importance for an insurer. Particular attention is paid to studying the right tail of the distribution, since it is important to not underestimate the size (and frequency) of large losses. The method of maximum likelihood is often used to estimate parameters of possible distributions, and various tests may be used to assess the fit of a proposed model (for example Kolmogorov-Smirnoff, and χ2 goodness-of-fit. Often one may find that a mixture of various distributions may be appropriate to model losses due to varying characteristics of both the policies and policyholders. The objective of this article is to call attention to a new approach to statistical modelling using quantile functions. This approach can deal with many issues associated with the steps of the statistical modelling process based on quantile methods. The definition and modelling of loss distributions in non-life insurance is one of the problem areas, where obtaining a good fit to the extreme tails of a distributional model is of major importance. It is a thesis of this article that the use of models based on quantiles provides an appropriate and flexible approach to the distributional modelling needed to obtain well-fitted tails. We are specifically interested in modelling and simulations the tails of loss distributions Thus is of particular relevance in reinsurance if we ale required to choose or price a high-excess layer. In this situation it is essential to find a good statistical model for the largest observed losses.