Mean-Preserving Increases in Risk and Three-Atom Spreads

Abstract

We show that a risk change from F(x) to G(x) is a mean-preserving increase in risk if and only if F(x) and G(x) are the weak limits of two sequences of discrete distributions {F_i(x)}_{i=1}^n and {G_i(x)}_{i=1}^n respectively such that for each i, the risk change from F_i(x) to G_i(x) can be decomposed into some mean-preserving three-atom spreads with all atoms from the set of atoms of the risk change.

Keywords: increasing risk, mean-preserving spread, spread, new construction

JEL Classification: D81