Varying Basic Probabilities

Abstract

In the preceding chapters it has been assumed, with minor exceptions, that the basic probability remains constant so that the number of claims each year has the same expected value n. Furthermore, it has been assumed that the underlying processes obeyed the laws (i) to (iii) of Chapter 2, i.e. the process is assumed to be a Poisson process, elementary or generalized, depending on whether the amount of one claim is a constant or a random variable. In addition it has been assumed that the distribution function S(z) of the amount of one claim is stable or at least independent of the number of claims. These assumptions are obviously an idealization of the practical situation.