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 over-estimating 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 other decreases, as the claim dependence grows. The paper also presents some computable bounds for these ruin probabilities that are intractable even in the simplest cases, and illustrates the performance of these bounds for the multivariate compound Poisson risk models with slightly or highly dependent MarshallOlkin exponential claim sizes.