On dependence of risks and stop-loss premiums

In this paper, we investigate the notion of multivariate dependence between individuals and its effect on the related stop-loss premiums. First, we consider the type of negative dependence between individuals in a portfolio that gives rise to the safest aggregate claims where the portfolio consists of m life insurance polices with each policy having a positive face amount during a certain reference period. We then apply the superadditive dependence ordering cursorily studied in the literature to compare the riskiness of portfolios. Part of the results in this paper are generalizations of the results in [Dhaene, J., Goovaerts, M.J., 1996. Dependency of risks and stop-loss order. ASTIN Bulletin 26, 201–212; Dhaene, J., Goovaerts, M.J., 1997. On the dependency of risks in the individual life model. Insurance: Mathematics and Economics 19, 243–253].