Choquet Integral with contamination∗

Suppose that an economic agent is (1 − ψi) · pi certain that uncertainty she faces on a certain event Ai is characterized by a particular probability which associates pi over this event (and similarly for all events), but that she has a fear that, with ψi · pi chance, her conviction over the event Ai is completely wrong and she is left perfectly ignorant about the true probability in the present as well in the future. This situation generalizes the so often called “ε-contamination”. The purpose of this paper is to investigate the general conditions under which a contam-ination of confidence of some probability measure can be represented through the probability measures in the core of a convex capacity. In the sequel it will be presented two new formulas of the Choquet Integral in a parametric approach (based on the ambiguity level) that gen-eralizes the well known formula of the expected value for the case of ε−contamination and can be applied to contaminations. A special property of the Choquet Integral (monotonicity of the ambiguity level) is also presented. JEL Classification: D81