Stop-loss order for portfolios of dependent risks

The paper considers the riskiness of portfolios of dependent risks. The supermodular stochastic order is used to compare the dependence of multivariate distributions with equal marginals. It is shown that supermodular ordering implies stop-loss order of the portfolios. Moreover, the riskiest portfolio under all portfolios with equal marginals is characterized. This extends the results of Dhaene and Goovaerts (1996, 1997).