Risk Aversion: Differential Conditions for the Concavity in Transformed Two-Parameter Distributions

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

No 2016:30, 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, that usually is the Expected value of the return, as a generic function of these two parameters. This paper determines the Differential Conditions for the definitions of Risk and Target that maintain the Concavity of the Expected Utility Function downward in the 3D space of the Risk, Target and Expected Utility Function. As a particular case, in the paper 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 the downward concavity property for the Expected Utility Function.

Keywords: Concavity; CRRA Utility Function; Expected Utility Function; Expected Shortfall; Differential Conditions; Quadratic Utility Function; Standard Deviation; Transformation Parametric Functions; Truncated Normal Distribution (search for similar items in EconPapers)
JEL-codes: G11 G14 G23 G24 (search for similar items in EconPapers)
Pages: 54 pages
Date: 2016
New Economics Papers: this item is included in nep-rmg and nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:ven:wpaper:2016:30

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