On Jensen's inequality for generalized Choquet integral with an application to risk aversion

Abstract

In the paper we give necessary and sufficient conditions for the Jensen inequality to hold for the generalized Choquet integral with respect to a pair of capacities. Next, we apply obtained result to the theory of risk aversion by providing the assumptions on utility function and capacities under which an agent is risk averse. Moreover, we show that the Arrow-Pratt theorem can be generalized to cover the case, where the expectation is replaced by the generalized Choquet integral.