Modeling and comparing dependencies in multivariate risk portfolios

In this paper we investigate multivariate risk portfolios where the risks are dependent. By providing 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 stoploss premiums. In particular some comparison results for portfolios with twopoint 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 in risk portfolios can have a severe impact on the stoploss premium. In fact we show that the effect of dependencies can grow beyond any given bound.