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