# On the Arrow-Pratt risk aversion model for the generalized Choquet integral

*Marek Kałuszka* and
*Wioletta Szeligowska*

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Marek Kałuszka: Politechnika Łódzka, Wydział Fizyki Technicznej, Informatyki i Matematyki Stosowanej

Wioletta Szeligowska: Politechnika Łódzka, Wydział Fizyki Technicznej, Informatyki i Matematyki Stosowanej

*Collegium of Economic Analysis Annals*, 2018, issue 51, 169-184

**Abstract:**
In the 1970s Kahneman and Tversky conducted a series of experiments which suggested that people do not behave accordingly to the von Neumann-Morgenstern’s Expected Utility Theory. Therefore, they proposed an alternative theory, called the Cumulative Prospect Theory, in which they used the Choquet integral with respect to distorted probability measures to describe decision making in risk and uncertainty conditions. The paper presents the generalized Arrow-Pratt risk aversion model, when the classic expected value is replaced by the generalized Choquet integral. To do this, we require necessary and sufficient conditions for the Jensen type inequality for the generalized Choquet integral with respect to arbitrary monotone measure, that is not an additive set function. We will provide some results of this type and point the difficulties that show up without the additivity assumption.

**Keywords:** Jensen inequality; generalized Choquet integral; nonadditive measure; capacity; risk aversion; measures of risk aversion (search for similar items in EconPapers)

**Date:** 2018

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**Persistent link:** https://EconPapers.repec.org/RePEc:sgh:annals:i:51:y:2018:p:169-184

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