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

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Listed:
  • Fausto Corradin

    (GRETA Associati, Venice)

  • Domenico Sartore

    (Department of Economics, Ca' Foscari University 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 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.

Suggested Citation

  • Fausto Corradin & Domenico Sartore, 2018. "Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions," Working Papers 2018:24, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2018:24
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    References listed on IDEAS

    as
    1. LiCalzi, Marco & Sorato, Annamaria, 2006. "The Pearson system of utility functions," European Journal of Operational Research, Elsevier, vol. 172(2), pages 560-573, July.
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    5. Fausto Corradin & Domenico Sartore, 2016. "Weak Dependence of CRRA on Standard Deviation in the Case of Truncated Normal Distribution of Returns," Working Papers 2016:18, Department of Economics, University of Venice "Ca' Foscari".
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    More about this item

    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;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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