Comparison of portfolios which depend on multivariate Bernoulli random variables with fixed marginals

Consider a portfolio consisting of n risks. An individual risk is a product of two random variables: (1) a Bernoulli random variable which is an indicator for the event that claim has occurred; (2) the claim amount, which is a positive random variable. In the first part of this paper, we extend the results of Hu and Wu [Insur. Math. Econ. 24 (1999) 323] and Dhaene and Goovaerts [Insur. Math. Econ. 19 (1997) 243] for the case of exchangeable Bernoulli random variables. In the second part, we introduce a new partial ordering between multivariate Bernoulli distributions with identical marginals. We apply this new ordering to compare the stop-loss premium of different portfolios.