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In the paper we give necessary and sufficient conditions for the Jenseninequality to hold for the generalized Choquet integral with respect to a pairof capacities. Next, we apply obtained result to the theory of risk aversion byproviding the assumptions on utility function and capacities under which anagent is risk averse. Moreover, we show that the Arrow-Pratt theorem can begeneralized to cover the case, where the expectation is replaced by thegeneralized Choquet integral.

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