An insurance company is considered as an intermediary between policyholders and the capital market. By applying the traditional and the generalized version of the capital asset pricing model, a class of premium principles can be derived. This class is fully compatible with Bühlmann's economic premium principle. Moreover, insurance premiums can be directly related to risk premiums on the stock exchange.

In the usual model of the collective risk theory, we are interested in the severity of ruin, as well as its probability. As a quantitative measure, we propose G(u, y), the probability that for given initial surplus u ruin will occur and that the deficit at the time of ruin will be less than y, and the corresponding density g(u, y). First a general answer in terms of the transform is obtained. Then, assuming that the claim amount distribution is a combination of exponential distributions, we determine g; here the roots of the equation that defines the adjustment coefficient play a central role. An explicit answer is also given in the case in which all claims are of constant size.

For the case of a portfolio with identical claim amount distributions, Gerber's error bound for the compound Poisson approximation is improved (in the case λ ⩾ 1). The result can also be applied to more general portfolios by partitioning them into homogeneous subportfolios.

Some reasons are given for paying special attention to the gross cost of catastrophe claims in planning and control. A method is then described of defining catastrophe claims and estimating their expected cost. The various steps in applying the method to real data and its performance for planning and control are discussed and illustrated in conjunction with an investigation carried out on a company portfolio.

A method is presented for projecting the development of reported losses, or of paid losses, or the number of reported cases, for each of the first 12 months of an accident year. The method is based on the relationship between development patterns after the first 12 months of an accident year and development patterns during the first 12 months. A way of deriving the development pattern of an individual accident quarter or accident month is also described.

It is pointed out that the method can be useful for underwriting decisions for which the most recent experience is relevant, or for estimating loss reserves at the end of a quarter or when earned premium differs greatly by month or quarter.

We compare three modern methods for calculating the aggregate claims distribution with respect to their computation amount and accuracy: Panjer's algorithm, the approximation method of Kornya and the most recent, exact procedure of De Pril. They are compared numerically in the case of actual Life portfolios. The computation amount of De Pril's method is much greater than that of the two others, which do not differ substantially in this respect. The accuracy of Kornya's and Panjer's methods is remarkably high in the examples considered. However, as the accuracy of Kornya's approximation method can be determined easily in advance, this procedure turns out to be the most useful one for the problems arising from practical work.