Dependence properties and bounds for ruin probabilities in multivariate compound risk models

In risk management, ignoring the dependence among various types of claims often results in overestimating or under-estimating the ruin probabilities of a portfolio. This paper focuses on three commonly used ruin probabilities in multivariate compound risk models, and using the comparison methods shows how some ruin probabilities increase, whereas the others decrease, as the claim dependence grows. The paper also presents some compatable bounds for these ruin probabilities, which can be calculated explicitly for multivariate phase-type distributed claims, and illustrates the performance of these bounds for the multivariate compound Poisson risk models with slightly or highly dependent Marshall-Olkin exponential claim sizes. (c) 2006 Elsevier Inc. All rights reserved.