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

Published Online:https://doi.org/10.1287/deca.2019.0404

References

  • Abramowitz M, Stegun IA (1966) Handbook of Mathematical Functions, Applied Mathematics Series, vol. 55 U.S. Department of Commerce, Washington, DC).CrossrefGoogle Scholar
  • Allais M (1953) Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’école Américaine. Econometrica 21(4):503–546.CrossrefGoogle Scholar
  • Albrecht P (2014) Risk measures. Wiley StatsRef: Statistics Reference Online (John Wiley & Sons, Hoboken, NJ), https://doi.org/10.1002/9781118445112.stat04713.Google Scholar
  • Al-Najjar C, Malakooti B (2020a) Application of geometric dispersion theory in decision-making for ambiguity. Working paper, Case Western Reserve University, Cleveland.Google Scholar
  • Al-Najjar C, Malakooti B (2020b) Application of geometric dispersion theory in decision-making for game theory. Working paper, Case Western Reserve University, Cleveland.Google Scholar
  • Ariely D (2008) Predictably Irrational (HarperCollins, New York).Google Scholar
  • Arrow KJ (1965) The theory of risk aversion. Aspects of the Theory of Risk Bearing (Yrjö Jahnssonin Foundation, Helsinki, Finland).Google Scholar
  • Baltussen G, Post T, van Vliet P (2006) Violations of cumulative prospect theory in mixed gambles with moderate probabilities. Management Sci. 52(8):1288–1290.LinkGoogle Scholar
  • Blavatskyy PR (2010) Modifying the mean-variance approach to avoid violations of stochastic dominance. Management Sci. 56(11):2050–2057.LinkGoogle Scholar
  • Blavatskyy PR (2012) The Troika paradox. Econom. Lett. 115(2):236–239.CrossrefGoogle Scholar
  • Brachinger HW, Weber M (1997) Risk as a primitive: A survey of measures of perceived risk. OR Spektrum 19(4):235–250.CrossrefGoogle Scholar
  • Birnbaum MH, Bahra JP (2007) Gain-loss separability and coalescing in risky decision making. Management Sci. 53(6):1016–1028.LinkGoogle Scholar
  • Borch K (1969) A note on uncertainty and indifference curves. Rev. Econom. Stud. 36(1):1–4.CrossrefGoogle Scholar
  • Camerer C, Ho TH (1999) Experience‐weighted attraction learning in normal form games. Econometrica 67(4):827–874.CrossrefGoogle Scholar
  • Chen Z, Wang Y (2008) Two-sided coherent risk measures and their application in realistic portfolio optimization. J. Banking Finance 32(12):2667–2673.CrossrefGoogle Scholar
  • Cobb CW, Douglas PH (1928) A theory of production. Amer. Econom. Rev. 18(1):139–165.Google Scholar
  • Coombs CH, Bowen JN (1971) A test of VE-theories of risk and the effect of the central limit theorem. Acta Psychologica 35(1):15–28.CrossrefGoogle Scholar
  • Coombs CH, Huang LC (1976) Tests of the betweenness property of expected utility. J. Math. Psych. 13(3):323–337.CrossrefGoogle Scholar
  • Fishburn PC (1979) On the foundations of mean-variance analyses. Theory Decision 10(1–4):99–111.CrossrefGoogle Scholar
  • Föllmer H, Schied A (2002) Convex measures of risk and trading constraints. Finance Stochastics 6(4):429–447.CrossrefGoogle Scholar
  • Gonzalez R, Wu G (1999) On the shape of the probability weighting function. Cognitive Psych. 38(1):129–166.CrossrefGoogle Scholar
  • Harrison GW, Rutström EE (2009) Representative agents in lottery choice experiments: One wedding and a decent funeral. Experiment. Econom. 12(2):133–158.CrossrefGoogle Scholar
  • Hecht D (2013) The neural basis of optimism and pessimism. Experiment. Neurobiology 22(3):173–199.CrossrefGoogle Scholar
  • Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2):263–292.CrossrefGoogle Scholar
  • Keller LR, Sarin RK, Weber M (1986) Empirical investigation of some properties of the perceived riskiness of gambles. Organ. Behav. Human Decision Processes 38(1):114–130.CrossrefGoogle Scholar
  • Klein NH, Oglethorpe JE (1987) Cognitive reference points in consumer decision making. Wallendorf M, Anderson P, eds. Advances in Consumer Research, vol. 14 (Association for Consumer Research, Provo, UT), 183–187.Google Scholar
  • Komaki M, Malakooti B (2020) Portfolio selection based on GDT models. Preprint, https://dx.doi.org/10.2139/ssrn.3317786.Google Scholar
  • Krokhmal P, Zabarankin M, Uryasev S (2011) Modeling and optimization of risk. Surveys Oper. Res. Management Sci. 16(2):49–66.CrossrefGoogle Scholar
  • Levy H (2008) First degree stochastic dominance violations: Decision weights and bounded rationality. Econom. J. 118(528):759–774.Google Scholar
  • Loomes G, Sugden R (1998) Testing different stochastic specifications of risky choice. Economica 65(260):581–598.CrossrefGoogle Scholar
  • Machina MJ (1982) “Expected utility” analysis without the independence axiom. Econometrica 50(2):277–323.CrossrefGoogle Scholar
  • Malakooti B (2012) Decision making process: Typology, intelligence, and optimization. J. Intelligent Manufacturing 23(3):733–746.CrossrefGoogle Scholar
  • Malakooti B (2014a) Operations and Production Systems with Multiple Objectives (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • Malakooti B (2014b) A synopsis of multiplicative Z utility theory for solving risk problems. Proc. 2014 Internat. Conf. Advanced Agile Manufacturing (Oakland University, Rochester, MI).Google Scholar
  • Malakooti B (2018) Geometric dispersion theory for decisions under risk: Accurate out-of-sample predictions and four distinct behavioral patterns. Preprint, submitted June 28, https://dx.doi.org/10.2139/ssrn.3193116. (Revised version to appear as Malakooti (2020)).Google Scholar
  • Malakooti B (2019) Web-supplement of geometric dispersion theory. Accessed January 1, 2020, https://www.dropbox.com/s/ojbysen960rm8xw/WEB%20Supplements%20Integd%20GDT-291.docx?dl=0.Google Scholar
  • Malakooti B (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.Google Scholar
  • Malakooti B, Zhou YQ (1994) Feedforward artificial neural networks for solving discrete multiple criteria decision making problems. Management Sci. 40(11):1542–1561.LinkGoogle Scholar
  • Malakooti B, Komaki M, Al-Najjar C (2019a) Special geometric dispersion theory of decision making under risk: Analysis of asymmetric, relativity, new predictable empirical behaviors, and risk trinity. Web supplement. Accessed January 1, 2020, https://www.dropbox.com/s/be7yh3maxjo4ibp/Websupp%20of%20Dispersion%20Paper-5-8-2019.docx?dl=0.Google Scholar
  • Malakooti B, Komaki M, Al-Najjar C (2019b) Dispersion theory of risk: Characteristics of geometric dispersions on continues probability distribution. Working paper, Case Western Reserve University, Cleveland.Google Scholar
  • Markowitz H (1952) Portfolio selection. J. Finance 7(1):77–91.Google Scholar
  • Markowitz HM (1959) Portfolio Selection: Efficient Diversification of Investments (John Wiley & Sons, New York).Google Scholar
  • Marschak J (1950) Rational behavior, uncertain prospects, and measurable utility. Econometrica 18(2):111–141.CrossrefGoogle Scholar
  • Pichler A (2017) A quantitative comparison of risk measures. Ann. Oper. Res. 254(1–2):251–275.CrossrefGoogle Scholar
  • Pratt JW (1964) Risk aversion in the small and in the large. Econometrica 32(1–2):122–136.CrossrefGoogle Scholar
  • Quiggin J (1982) A theory of anticipated utility. J. Econom. Behav. Organ. 3(4):323–343.CrossrefGoogle Scholar
  • Rachev S, Ortobelli S, Stoyanov S, Fabozzi FJ, Biglova A (2008) Desirable properties of an ideal risk measure in portfolio theory. Internat. J. Theoret. Appl. Finance 11(1):19–54.CrossrefGoogle Scholar
  • Rasmusen E, Petrakis E (1992) Defining the mean-preserving spread: 3-pt vs. 4-pt. Decision Making Under Risk and Uncertainty (Springer, Dordrecht, Netherlands), 53–58.Google Scholar
  • Rockafellar RT, Uryasev SP, Zabarankin M (2002) Deviation measures in risk analysis and optimization. Working paper, Department of Industrial and Systems Engineering, University of Florida, Gainesville.Google Scholar
  • Rockafellar RT, Uryasev S, Zabarankin M (2006) Generalized deviations in risk analysis. Finance Stochastics 10(1):51–74.CrossrefGoogle Scholar
  • Rothschild M, Stiglitz JE (1970) Increasing risk: I. A definition. J. Econom. Theory 2(3):225–243.CrossrefGoogle Scholar
  • Sarin RK, Weber M (1993) Risk-value models. Eur. J. Oper. Res. 70(2):135–149.CrossrefGoogle Scholar
  • Schreider S, Zeephongsekul P, Abbasi B, Fernandes M (2013) Game theoretic approach for fertilizer application: Looking for the propensity to cooperate. Ann. Oper. Res. 206(1):385–400.CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory (Society for Industrial and Applied Mathematics, Philadelphia).CrossrefGoogle Scholar
  • Sheikh S, Komaki M, Malakooti B (2015) Integrated risk and multi-objective optimization of energy systems. Comput. Indust. Engrg. 90(December):1–11.CrossrefGoogle Scholar
  • Starmer C (2000) Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk. J. Econom. Lit. 38(2):332–382.CrossrefGoogle Scholar
  • Thaler R (1980) Toward a positive theory of consumer choice. J. Econom. Behav. Organ. 1(1):39–60.CrossrefGoogle Scholar
  • Tversky A, Kahneman D (1992) Advances in prospect theory: Cumulative representation of uncertainty. J. Risk Uncertainty 5(4):297–323.CrossrefGoogle Scholar
  • Wu G, Markle AB (2008) An empirical test of gain-loss separability in prospect theory. Management Sci. 54(7):1322–1335.LinkGoogle Scholar
  • Van Heerwaarden AE, Kaas R (1992) The Dutch premium principle. Insurance, Math. Econom. 11(2):129–133.CrossrefGoogle Scholar
  • von Neumann J, Morgenstern O (1944) Theory of Games and Economic Behavior (Princeton University Press, Princeton, NJ).Google Scholar
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