Risk Aversion: Differential Conditions for the Concavity in Transformed Two-Parameter Distributions
54 Pages Posted: 14 Nov 2016
Date Written: November 3, 2016
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: Suggested Citation