Monotonicity results for portfolios with heterogeneous claims arrival processes

Loosely speaking, actuaries believe that the heterogeneity of the risks tends to increase dangerousness. This in turn leads to requiring more economic capital. This paper aims to formalize this intuitive idea. More specifically, vectors of compound sums will be considered, with different claim frequency distributions and/or different claim severity distributions. The effect of increasing the heterogeneity will be studied with the help of majorization. Various multivariate integral stochastic orderings will be used to compare situations according to their level of heterogeneity.