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

54 Pages Posted: 14 Nov 2016

See all articles by Fausto Corradin

Fausto Corradin

GRETA Associati

Domenico Sartore

Ca Foscari University of Venice - Dipartimento di Economia

Date Written: November 3, 2016

Abstract

The condition of Risk Aversion implies that the Utility Function must be concave. Taking into account the dependence of the Utility Function on the wealth that in turn depends on the return, we consider a return with any type of two-parameter distribution. It is possible to define Risk and Return as a generic function of these two parameters. This paper determines the Differential Conditions for the definitions of Risk and Return that maintain the Risk Aversion property in the 3D space of the Risk, Return 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.

Keywords: utility function, expected utility function, risk aversion, transformation, parametric functions, differential condition, Jacobian, truncated normal distribution

JEL Classification: G11, G14, G23, G24

Suggested Citation

Corradin, Fausto and Sartore, Domenico, Risk Aversion: Differential Conditions for the Concavity in Transformed Two-Parameter Distributions (November 3, 2016). Available at SSRN: https://ssrn.com/abstract=2869030 or http://dx.doi.org/10.2139/ssrn.2869030

Fausto Corradin

GRETA Associati ( email )

San Marco 3870
Venezia, 30124
Italy

Domenico Sartore (Contact Author)

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

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