Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions

Fausto Corradin () and Domenico Sartore
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Fausto Corradin: GRETA Associati, Venice

No 2018:24, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

Abstract: The condition of Risk Aversion implies that the Utility Function must be concave. We take into account the dependence of the Utility Function on the return that has any type of two-parameter distribution; it is possible to define Risk and Target, the former may be the Standard Deviation of the return, and the latter is usually the Expected value of the return, as a generic function of these two parameters. Considering the 3D space of Risk, Target and Expected Utility, this paper determines the Differential Conditions for these three functions so that the Expected Utility Function depends decreasingly on Risk and increasingly on Target, that means the iso-utility curves have positive slope in the plane of Risk and Target. As a specific case, we discuss these conditions in the case of the CRRA Utility Function and the Truncated Normal distribution. Furthermore, different measures of Risk are chosen, such as Value at Risk (VaR) and Expected Shortfall (ES), to verify if these measures maintain a positive slope of the iso-utility curves in the Risk-Target plane.

Keywords: Concavity; CRRA; Differential Condition; Expected Shortfall; Expected Utility Function; Quadratic Utility Function; Risk Aversion; Standard Deviation; Transformation of Parametric Functions; Truncated Normal distribution; Value at Risk (search for similar items in EconPapers)
JEL-codes: G11 G14 G23 G24 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2018
New Economics Papers: this item is included in nep-rmg and nep-upt
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Related works:
Journal Article: Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:ven:wpaper:2018:24

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