Cumulative prospect theory on countable state space

Abstract

The cumulative prospect theory (CPT) holds if the preference on the set of prospects is represented by the difference of two Choquet integrals. The CPT with countable state space and finite support of a prospect is considered. It is shown that the functional with the comonotonic additivity and comonotonic monotonicity, which is a weaker condition than monotonicity, is is a rank- and sign-dependent functional ( r.s.d. functional), that is, the difference of two Choquet integrals. Applying this result, we present the conditions for a preference relation to be CPT.