A note on “Re-examining the law of iterated expectations for Choquet decision makers”

Abstract

This note completes the main result of Zimper (Theory and decision, doi: 10.1007/s11238-010-9221-8 , 2010), by showing that additional conditions are needed in order the law of iterated expectations to hold true for Choquet decision makers. Due to the comonotonic additivity of Choquet expectations, the equation E[f, ν(dω)] = E[E[f(ω i, j ), ν(A i, j |A i )], ν(A i )], is valid only when the act f is comonotonic with its dynamic form, that we name “conditional certainty equivalent act”.