Modeling and Comparing Dependencies in Multivariate Risk Portfolios

In this paper we investigate multivariate risk portfolios, where the risks are dependent. By proving some natural models for risk portfolios with the same marginal distributions we are able to compare two portfolios with different dependence structure with respect to their stop-loss premiums. In particular, some comparison results for portfolios with two-point distributions are obtained The analysis is based on the concept of the so-called supermodular ordering. We also give some numerical results which indicate that dependencies m risk portfolios can have a severe impact on the stop-loss premium. In fact, we show that the effect of dependencies can grow beyond any given bound. Keywords: Dependent risks; Stop-loss premium, Supermodular order; Stop-loss order; Exchangeable Bernoulli random variables