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Advances in Decision Sciences (ADS)

Advances in Decision Sciences (ADS)

Published by Asia University, Taiwan; Scientific and Business World

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

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

Title

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

Authors

  • Fausto Corradin
    (GRETA Associates, University Ca’ Foscari of Venice)
  • Domenico Sartore
    (University Ca’ Foscari of Venice)

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 first one may be the Standard Deviation of the return and the last one usually is 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 particular 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, 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, Differential Conditions, Expected Shortfall, Risk Aversion, Standard Deviation, Value at Risk

Classification-JEL

G11, G14, G23, G24

Pages

142-217

https://doi.org/10.47654/v24y2020i3p142-217

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ISSN 2090-3359 (Print)
ISSN 2090-3367 (Online)

Asia University, Taiwan

Scientific and Business World

4.7
2023CiteScore
 
86th percentile
Powered by  Scopus
SCImago Journal & Country Rank
Q2 in Scopus
CiteScore 2023 = 4.7
CiteScoreTracker 2024 = 8.5
SNIP 2023 = 0.799
SJR Quartile = Q1
SJR 2024 = 0.814
H-Index = 20

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