Hey,

does anyone know if there exist some conditions on the variance and mean of normally distributed random variables $\displaystyle X,Y$ such that it holds

$\displaystyle Ef(X) \leq Ef(Y)$ for $\displaystyle f$ quasi-convex (but not convex)?

Unfortunatly, I am not very familiar with stochastic orders (convex, increasing convex,..) so far. I just started familiarizing myself with it using the book of Mueller "Comparison Methods for Stochastic Models and Risks". Can anyone recommend other books/papers?

Thanks in advance!