Description: In this paper some general properties of compound nonstationary Poisson processes are discussed as well as the possible shapes of the intensity function. A decomposition of the accumulated claims as a sum of independent compound Poisson sums is shown. An embedded discrete risk model is introduced. It is shown that ruin probabilities and maximal losses for the nonstationary risk model find lower bounds with the embedded discrete model. From Actuarial Research Clearing House 1994 VOL. 1.

Description: Two renewal processes, known in reliability maintenance as minimal repair and replacement policy, are introduced in this paper. Their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate. Applications in risk theory are shown. From Actuarial Research Clearing House 1993, VOL. 1.