Tail behavior of randomly weighted sums with interdependent summands (2503.11271v1)

Abstract: We reconsider a classical, well-studied problem from applied probability. This is the max-sum equivalence of randomly weighted sums, and the originality is because we manage to include interdependence among the primary random variables, as well as among primary random variables and random weights, as a generalization of previously published results. As a consequence we provide the finite-time ruin probability, in a discrete-time risk model. Furthermore, we established asymptotic bounds for the generalized moments of randomly weighted sums in the case of dominatedly varying primary random variables under the same dependence conditions. Finally, we give some results for randomly weighted and stopped sums under similar dependence conditions, with the restriction that the random weights are identically distributed, and the same holds for the primary random variables. Additionally, under these assumptions, we find asymptotic expressions for the random time ruin probability, in a discete-time risk model.