On a correlated aggregate claims model with thinning-dependence structure

Abstract

In this paper, we consider a risk model with n (n ≥ 2) dependent classes of insurance business. Stochastic sources related to claim occurrences of the n classes are classified into m groups. It is assumed that each event in the k th (k = 1, 2,..., m) group may cause a claim in the jth class (j = 1, 2,..., n) with a certain probability. Within this framework, there exists certain correlation between the n claim-number processes due to the so-called thinning-dependence structure. We examine basic properties of the proposed risk process and study upper bounds for the ruin probability under certain assumptions. We also investigate the impact of the thinning-dependence structure as well as that of the classification of the stochastic sources on the ruin probability. © 2005 Elsevier B.V. All rights reserved.