A Generalized Model for the Risk Process and its Application to a Tentative Evaluation of Outstanding Liabilities

A compound Poisson process, in this context abbreviated to cPp, is defined by a probability distribution of the number m of events in the interval (o, "r) of the original scale of the process parameter, assumed to be one-dimensional, in the following form. (forum) (1) where (variable) du shall be inserted for t, X. being the intensity function of a Poisson process with the expected number t of events in the interval (o, .) and U(v, ,~) is the distribution function of v for every fixed value of ~, here called the risk distribution. If the inverse of f Xu du = t is substituted for t, in the right membrum of (I), the function obtained is a function of t.