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Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad

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  • Behnam Malakooti

    (Department of Electrical, Computers, and Systems Engineering, Case Western Reserve University, Cleveland, Ohio 44106)

  • Mohamed Komaki

    (Marketing and Business Analytics Department, College of Business, Texas A&M University–Commerce, Commerce, Texas 75428)

  • Camelia Al-Najjar

    (Department of Electrical, Computers, and Systems Engineering, Case Western Reserve University, Cleveland, Ohio 44106)

Abstract

Many studies have spotlighted significant applications of expected utility theory (EUT), cumulative prospect theory (CPT), and mean-variance in assessing risks. We illustrate that these models and their extensions are unable to predict risk behaviors accurately in out-of-sample empirical studies. EUT uses a nonlinear value (utility) function of consequences but is linear in probabilities, which has been criticized as its primary weakness. Although mean-variance is nonlinear in probabilities, it is symmetric, contradicts first-order stochastic dominance, and uses the same standard deviation for both risk aversion and risk proneness. In this paper, we explore a special case of geometric dispersion theory (GDT) that is simultaneously nonlinear in both consequences and probabilities. It complies with first-order stochastic dominance and is asymmetric to represent the mixed risk-averse and risk-prone behaviors of the decision makers. GDT is a triad model that uses expected value, risk-averse dispersion, and risk-prone dispersion. GDT uses only two parameters, z and z X ; these constants remain the same regardless of the scale of risk problem. We compare GDT to several other risk dispersion models that are based on EUT and/or mean-variance, and identify verified risk paradoxes that contradict EUT, CPT, and mean-variance but are easily explainable by GDT. We demonstrate that GDT predicts out-of-sample empirical risk behaviors far more accurately than EUT, CPT, mean-variance, and other risk dispersion models. We also discuss the underlying assumptions, meanings, and perspectives of GDT and how it reflects risk relativity and risk triad. This paper covers basic GDT, which is a special case of general GDT of Malakooti [Malakooti (2020) Geometric dispersion theory of decision making under risk: Generalizing EUT, RDEU, & CPT with out-of-sample empirical studies. Working paper, Case Western Reserve University, Cleveland.].

Suggested Citation

  • Behnam Malakooti & Mohamed Komaki & Camelia Al-Najjar, 2021. "Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad," Decision Analysis, INFORMS, vol. 18(1), pages 41-77, March.
    • Handle: RePEc:inm:ordeca:v:18:y:2021:i:1:p:41-77
    DOI: 10.1287/deca.2019.0404
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