In this paper we shall study the problem of determining “correct” premium rates for sub-groups of an insurance collective. This problem obviously occurs in all branches of insurance. However, it seems at present to be a really burning issue in automobile insurance. We shall show that the problem can be formulated as a conflict between groups which can gain by co-operating, although their interests are opposed. When formulated in this way, the problem evidently can be analysed and solved by the help ot the “Game Theory” of Von Neumann and Morgenstern (5).

We shall first illustrate the problem by a simple example. We consider a group of n1 = 100 persons, each of whom may suffer a loss of 1, with probability p1 = 0.1. We assume that these persons consider forming an insurance company to cover themselves against this risk. We further assume that for some reason, government regulations or prejudices of managers, an insurance company must be organized so that the probability of ruin is less than 0.001

If such a company is formed, expected claim payment will be

and the standard deviation of the claim payments will be

If the government inspection (or the company's actuary) agrees that the ruin probability can be calculated with sufficient approximation by assuming that the claim payments have a normal distribution, the company must have funds amounting to