I've been searching for some knowledge on ordering of sums of quantiles. I've found some requirements such that, for RVs X, Y:
Cq(X + Y) > Cq(X) + Cq(Y)
However, I need to find out for what RVs X, Y, Z the following holds:
Cq(X + Y + Z)/(Cq(X) + Cq(Y) + Cq(Z)) > Cq(X + Y)/(Cq(X) + Cq(Y))
I need this result for a game theoretic problem with quantile utility functions. Anyone has any idea for what RVs this would hold?
Any help is appreciated. Thanks!