A formula, originally presented by Haldane (1938), for the evaluation of the distribution of aggregate claims is examined and compared with some other approaches. The idea is to apply a symmetrizing transformation to the original variable in order to make it susceptible to be approximated by the normal distribution.

In the present paper we present two credibility regression models for the classification of passenger cars. As regressors we use technical variables like price, weight, etc. In both models we derive credibility estimators and find expressions for their estimation errors. Estimators for structure parameters are proposed. A numerical example based on real data is given. The second model is hierarchical with a level for make of car.

We study the linear Markov property, i.e. the possibility of basing the credibility estimator on data of the most recent time period without loss of accuracy. Necessary and sufficient conditions are derived generally. The meaning of the linear Markov property is also discussed in different experience rating and loss reserving models.

The authors challenge the traditional balance sheet concept of the solvency of a general insurance company and put forward an emerging costs concept, which enables the true nature of the assets and liabilities to be taken into account, including their essential variability. Simulation is suggested as a powerful tool for use in examining the financial strength of a company. A simulation model is then used to explore the resilience of a company's financial position to a variety of possible outcomes and to assess the probability that the assets will prove adequate to meet the liabilities with or without an assumption of continuing new business. This suggests the need for an appropriate asset margin assessed individually for each company. The implications for the management and supervision of general insurance companies are explored. The suggestion is made that the effectiveness of supervision based on the balance sheet and a crude solvency margin requirement is limited. More responsibility should be placed on an actuary or other suitably qualified professional individual to report on the overall financial strength of the company, both to management and to the supervisory authorities.