The paper considers several types of dependencies between the differen
t risks of a life insurance portfolio. Each policy is assumed to have
a positive face amount (or an amount at risk) during a certain referen
ce period. The amount is due if the policy holder dies during the refe
rence period. First, we will look for the type of dependency between i
ndividuals that gives rise to the riskiest aggregate claims in the sen
se that it leads to the largest stop-loss premiums. Further, this resu
lt is used to derive results for weaker forms of dependency, where the
only non-independent risks of the portfolio are the risks of couples.