On the computation of the aggregate claims distribution in the individual life model with bivariate dependencies

In this paper, we focus on the computation of the aggregate claims distribution in the individual life model when the portfolio is composed of independent pairs of dependent risks. We prove that the bivariate probabilities associated to each couple under any intermediate positive (negative) dependency hypothesis about their mortality can always be written as a convex linear combination between the independent and the comonotonic (mutually exclusive) ones. Considering this structure for the bivariate probabilities, we then obtain two recursive schemes for computing the distribution of the aggregate claims of the portfolio. These recursions greatly facilitate the computation of the aggregate claims distribution of a life insurance (sub)portfolio exclusively composed of dependent couples, and ease the interpretation of the impact of the dependence on the associated stop-loss premiums. Numerical results are given to demonstrate the applicability and efficiency of the method.