A Distribution Free Method for General Risk Problems

In practical applications of the collective theory of risk one is very often confronted with the problem of making some kind of assumptions about the form of the distribution functions underlying the frequency as well as the seventy of claims Lundberg's [6] and Cramer's [3] approach are essentially based upon the hypothesis that the number of claims occurring in a certain period obey the Poisson distribution whereas for the conditional distribution of the amount claimed upon occurrence of such a claim the exponential distribution is very often used Of course, by weighting the Polsson distributions (as e g done by Ammeter [I]) one enlarges the class of "frequency of claims" distributions considerably but nevertheless there remains an uneasy feeling about artificial assumptions, which are just made for mathematical convenience but are not necessarily related to the practical problems to which the theory of risk is applied.