10th Anniversary Special IssueView this Special Issue
Wing-Keung Wong, "Stochastic dominance theory for location-scale family", Advances in Decision Sciences, vol. 2006, Article ID 082049, 10 pages, 2006. https://doi.org/10.1155/JAMDS/2006/82049
Stochastic dominance theory for location-scale family
Meyer (1987) extended the theory of mean-variance criterion to include the comparison among distributions that differ only by location and scale parameters and to include general utility functions with only convexity or concavity restrictions. In this paper, we make some comments on Meyer's paper and extend the results from Tobin (1958) that the indifference curve is convex upwards for risk averters, concave downwards for risk lovers, and horizontal for risk neutral investors to include the general conditions stated by Meyer (1987). We also provide an alternative proof for the theorem. Levy (1989) extended Meyer's results by introducing some inequality relationships between the stochastic-dominance and the mean-variance efficient sets. In this paper, we comment on Levy's findings and show that these relationships do not hold in certain situations. We further develop some properties among the first- and second-degree stochastic dominance efficient sets and the mean-variance efficient set.
- G. Anderson, “Toward an empirical analysis of polarization,” Journal of Econometrics, vol. 122, no. 1, pp. 1–26, 2004.
- D. P. Baron, “On the utility theoretic foundations of mean-variance analysis,” Journal of Finance, vol. 32, no. 5, pp. 1683–1697, 1977.
- U. Broll, J. E. Wahl, and W.-K. Wong, “Elasticity of risk aversion and international trade,” Economics Letters, vol. 91, no. 1, pp. 126–130, 2006.
- K. V. Chow, “Marginal conditional stochastic dominance, statistical inference, and measuring portfolio performance,” Journal of Financial Research, vol. 24, no. 2, pp. 289–307, 2001.
- A. M. Dillinger, W. E. Stein, and P. J. Mizzi, “Risk averse decisions in business planning,” Decision Sciences, vol. 23, no. 4, pp. 1003–1008, 1992.
- M. Doumpos, S. Zanakis, and C. Zopounidis, “Multicriteria preference disaggregation for classification problems with an application to global investing risk,” Decision Sciences, vol. 32, no. 2, pp. 333–385, 2001.
- M. S. Feldstein, “Mean-variance analysis in the theory of liquidity preference and portfolio selection,” Review of Economics Studies, vol. 36, no. 1, pp. 5–12, 1969.
- W. M. Fong and W.-K. Wong, “The modified mixture of distributions model: a revisit,” Annals of Finance, vol. 2, no. 2, pp. 167–178, 2006.
- W. M. Fong, W.-K. Wong, and H. H. Lean, “International momentum strategies: a stochastic dominance approach,” Journal of Financial Markets, vol. 8, no. 1, pp. 89–109, 2005.
- J. Hadar and W. R. Russell, “Stochastic dominance and diversification,” Journal of Economic Theory, vol. 3, no. 3, pp. 288–305, 1971.
- J. S. Hammond, “Simplifying the choice between uncertain prospects where preference is nonlinear,” Management Science, vol. 20, no. 7, pp. 1047–1072, 1974.
- G. Hanoch and H. Levy, “Efficiency analysis of choices involving risk,” Review of Economic Studies, vol. 36, no. 3, pp. 335–346, 1969.
- J. C. Hershey and P. J. H. Schoemaker, “Risk taking and problem context in the domain of losses: an expected utility analysis,” Journal of Risk and Insurance, vol. 47, no. 1, pp. 111–132, 1980.
- D. Kahneman and A. Tversky, “Prospect theory: an analysis of decision under risk,” Econometrica, vol. 47, no. 2, pp. 263–291, 1979.
- T. Kuosmanen, “Efficient diversification according to stochastic dominance criteria,” Management Science, vol. 50, no. 10, pp. 1390–1406, 2004.
- H. Levy, “Two-moment decision models and expected utility maximization: comment,” American Economic Review, vol. 79, no. 3, pp. 597–600, 1989.
- M. Levy and H. Levy, “Prospect theory: much ado about nothing?,” Management Science, vol. 48, no. 10, pp. 1334–1349, 2002.
- H. Levy and M. Levy, “Prospect theory and mean-variance analysis,” Review of Financial Studies, vol. 17, no. 4, pp. 1015–1041, 2004.
- H. Levy and Z. Wiener, “Stochastic dominance and prospect dominance with subjective weighting functions,” Journal of Risk and Uncertainty, vol. 16, no. 2, pp. 147–163, 1998.
- C.-K. Li and W.-K. Wong, “Extension of stochastic dominance theory to random variables,” RO Recherche Opérationnelle, vol. 33, no. 4, pp. 509–524, 1999.
- H. M. Markowitz, “Portfolio selection,” Journal of Finance, vol. 7, no. 1, pp. 77–91, 1952.
- E. M. Matsumura, K. W. Tsui, and W.-K. Wong, “An extended multinomial-Dirichlet model for error bounds for dollar-unit sampling,” Contemporary Accounting Research, vol. 6, no. 2, pp. 485–500, 1990.
- J. R. McNamara, “Portfolio selection using stochastic dominance criteria,” Decision Sciences, vol. 29, no. 4, pp. 785–801, 1998.
- J. Meyer, “Second degree stochastic dominance with respect to a function,” International Economic Review, vol. 18, no. 2, pp. 477–487, 1977.
- J. Meyer, “Two-moment decision models and expected utility maximization,” American Economic Review, vol. 77, no. 3, pp. 421–430, 1987.
- J. Meyer, “Two-moment decision models and expected utility maximization: reply,” American Economic Review, vol. 79, no. 3, p. 603, 1989.
- M. Myagkov and C. R. Plott, “Exchange economies and loss exposure: experiments exploring prospect theory and competitive equilibria in market environments,” American Economic Review, vol. 87, no. 5, pp. 801–828, 1997.
- T. Post, “Empirical tests for stochastic dominance efficiency,” The Journal of Finance, vol. 58, no. 5, pp. 1905–1931, 2003.
- G. V. Post and J. D. A. Diltz, “A stochastic dominance approach to risk analysis of computer systems,” MIS Quarterly, vol. 10, no. 4, pp. 362–375, 1986.
- T. Post and H. Levy, “Does risk loving drive asset prices? a stochastic dominance analysis of aggregate investor preferences and beliefs,” Review of Financial Studies, vol. 18, no. 3, pp. 925–953, 2005.
- M. Rothschild and J. E. Stiglitz, “Increasing risk. I. A definition,” Journal of Economic Theory, vol. 2, no. 3, pp. 225–243, 1970.
- M. Rothschild and J. E. Stiglitz, “Increasing risk. II. Its economic consequences,” Journal of Economic Theory, vol. 3, no. 1, pp. 66–84, 1971.
- W. F. Sharpe, “A simplified model for portfolio analysis,” Management Science, vol. 9, no. 2, pp. 277–293, 1963.
- H.-W. Sinn, Economic Decisions under Uncertainty, vol. 32 of Studies in Mathematical and Managerial Economics, North-Holland, Amsterdam, 1983.
- D. Stoyan, Comparison Methods for Queues and Other Stochastic Models, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, Chichester, 1983.
- L. Tesfatsion, “Stochastic dominance and the maximization of expected utility,” Review of Economic Studies, vol. 43, no. 2, pp. 301–315, 1976.
- J. Tobin, “Liquidity preference as behavior towards risk,” Review of Economics Studies, vol. 25, no. 2, pp. 65–86, 1958.
- A. Tversky and D. Kahneman, “Advances in prospect theory: cumulative representation of uncertainty,” Journal of Risk and Uncertainty, vol. 5, no. 4, pp. 297–323, 1992.
- J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, New Jersey, 1944.
- J. K. Weeks, “Stochastic dominance: a methodological approach to enhancing the conceptual foundations of operations management theory,” Academy of Management Review, vol. 10, no. 1, pp. 31–38, 1985.
- J. K. Weeks and T. R. Wingler, “A stochastic dominance ordering of scheduling rules,” Decision Sciences, vol. 10, no. 2, pp. 245–257, 1979.
- W.-K. Wong and G. Bian, “Robust estimation in capital asset pricing model,” Journal of Applied Mathematics and Decision Sciences, vol. 4, no. 1, pp. 65–82, 2000.
- W.-K. Wong and R. H. Chan, “On the estimation of cost of capital and its reliability,” Quantitative Finance, vol. 4, no. 3, pp. 365–372, 2004.
- W.-K. Wong and C.-K. Li, “A note on convex stochastic dominance,” Economics Letters, vol. 62, no. 3, pp. 293–300, 1999.
- Y. Zhao and W. Ziemba, “A dynamic asset allocation model with downside risk control,” Journal of Risk, vol. 3, no. 1, pp. 91–113, 2000.
Copyright © 2006 Wing-Keung Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.