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

TL;DR

This paper establishes conditions for Jensen's inequality to hold for the generalized Choquet integral, and applies these results to characterize risk aversion and generalize the Arrow-Pratt theorem in decision theory.

Contribution

It provides necessary and sufficient conditions for Jensen's inequality for the generalized Choquet integral and extends the Arrow-Pratt theorem to this setting.

Findings

Jensen's inequality holds under specific conditions for the generalized Choquet integral.

Risk aversion can be characterized using these integral conditions and utility functions.

The Arrow-Pratt theorem is generalized to the context of the generalized Choquet integral.

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.