On the increasing convex order of generalized aggregation of dependent random variables

Abstract

In this article, we study stochastic properties of the generalized sum of right tail weakly stochastic arrangement increasing (RWSAI) nonnegative random variables accompanied with stochastic arrangement increasing (SAI) Bernoulli variables. In terms of monotonicity, supermodularity/submodularity, and convexity of the bivariate kernel function, sufficient conditions are developed for the increasing convex ordering on the generalized aggregation. Applications in actuarial science including the individual risk model and the reserving capital allocation are presented to highlight our results.