Notes on collective risk theory

Abstract

Abstract A complete proof of existence of a probability measure m the space Ω of all sample functions was given by Cramér [4]. For a finitc period, a simplified proof was given in my paper [2]. The latter proof could be restricted to the space of sample functions having only a finite number of jumps, as the probability of an infinite number of jumps is zero in this case. In fact, dividing the space Ω into disjunct subspaces Ωn containing exactly n jumps we have: The measure of Ωn m the case of a finite period of length x is: Thus and consequently P (Ω∞) = 0. Therefore the set Ω∞ and all its subsets can be neglected.