On Distributions of Runs in the Compound Binomial Risk Model

Abstract

This paper is concerned with the distribution of runs associated with claim indicators in a compound binomial risk model. We study the total number of claims, the longest run without claim, the shortest run without claim and the total number of runs up to a fixed period before the occurrence of a ruin. These quantities are potentially useful for an investment strategy of an insurance company and for understanding the behavior of a specific portfolio over time. We obtain recursive equations for the exact distributions of these random variables. We also illustrate the theoretical results with numerical computations.