Risk terminology varies from organisation to organisation, and actuaries working in different organisations may use different terms to refer to the same risk, or use the same nomenclature for completely different risks. This paper sets out a classification system developed by the Risk Classification Working Party for the Profession that can be used as a common reference point for discussing risk. Actuaries will not be required to use this system, but it is hoped that common terminology will reduce the possibility of confusion in discussing risks.

We undertake a mathematical clarification of the QIS5 proposal for the calculation of the Motor Third Party Liability (MTPL) man-made catastrophe risk capital in terms of two more general models. The QIS5 model assumption implies that the total loss consists of a single catastrophe claim in case it occurs during the next one-year insurance time period. However, the total loss should instead be dynamically modelled by a sequence of claims of varying size that follow a compound Poisson Pareto model, which is our first alternative model. A second possibility also takes into account the effect of investments, whose financial return process follows a Black-Scholes-Merton model. If one excludes limits of coverage, then asymptotically as the total loss increases without limits the first model is equivalent to the model assumption obtained from the QIS5 assumption by replacing a single catastrophe claim by the total loss. In other words, the QIS5 simple model is justified as limiting asymptotic approximation to the classical compound Poisson Pareto model. Conversely, an asymptotic approximation to the VaR economic capital from this model identifies with a modified QIS5 CAT formula. The inclusion of limits of coverage is also analyzed. In this situation we obtain new simple closed-form implementations of the economic capital formulas.

A statistical analysis is performed on natural events which can produce important damages to insurers. The analysis is based on hurricanes which have been observed in the United States between 1954 et 1986.

At first, independence between the number and the amount of the losses is examined. Different distributions (Poisson and negative binomial for frequency and exponential, Pareto and lognormal for severity) are tested. Along classical tests as chi-square, Kolmogorov-Smirnov and non parametric tests, a test with weights on the upper tail of the distribution is used: the Anderson – Darling test.

Confidence intervals for the probability of occurrence of a claim and expected frequency for different potential levels of claims are derived. The Poisson Log-normal model gives a very good fit to the data.