Guo, Xu and Wong, WingKeung (2016): Multivariate Stochastic Dominance for Risk Averters and Risk Seekers.

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Abstract
This paper first extends some wellknown univariate stochastic dominance results to multivariate stochastic dominances (MSD) for both risk averters and risk seekers, respectively, to n order for any n ≥ 1 when the attributes are assumed to be independent and the utility is assumed to be additively and separable. Under these assumptions, we develop some properties for MSD for both risk averters and risk seekers. For example, we prove that MSD are equivalent to the expectedutility maximization for both risk averters and risk seekers, espectively. We show that the hierarchical relationship exists for MSD. We establish some dual relationships between the MSD for risk averters and risk seekers. We develop some properties for nonnegative combinations and convex combinations random variables of MSD and develop the theory of MSD for the preferences of both risk averters and risk seekers on diversification. At last, we discuss some MSD relationships when attributes are dependent and discuss the importance and the use of the results developed in this paper.
Item Type:  MPRA Paper 

Original Title:  Multivariate Stochastic Dominance for Risk Averters and Risk Seekers 
Language:  English 
Keywords:  Multivariate Stochastic Dominance, Risk Averters, Risk Seekers, Ascending stochastic dominance, descending stochastic dominance, utility function 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions 
Item ID:  70637 
Depositing User:  WingKeung Wong 
Date Deposited:  14 Apr 2016 06:53 
Last Modified:  28 Sep 2019 09:15 
References:  Bai, Z.D., Li, H., McAleer, M., Wong, W.K., 2015. Stochastic Dominance Statistics for Risk Averters and Risk Seekers: An Analysis of Stock Preferences for USA and China. Quantitative Finance 15(5), 889900. Bai, Z.D., LiU, H.X., Wong, W.K., 2009. Enhancement of the Applicability of Markowitz's Portfolio Optimization by Utilizing Random Matrix Theory. Mathematical Finance 19(4), 639667. Cox, J.C., 1973. A Theorem on AdditivelySeparable QuasiConcave Functions. Journal of Economic Theory 6(2), 210212. Davidson, R., Duclos, J.Y., 2000. Statistical inference for stochastic dominance and for the measurement of poverty and inequality. Econometrica 68, 14351464. De Miguel, V., Garlappi, L., Uppal, R., 2009. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? The Review of Financial Studies 22(5), 19151953. Denuit, M., Eeckhoudt, L., 2010. Bivariate stochastic dominance and substitute risk (in)dependent utilities. Decision Analysis 7(3), 302312. Dentcheva, D., Ruszczynski, A. 2003. Optimization with stochastic dominance constraints, SIAM J. Optim., 14, 548566. Dentcheva, D., Ruszczynski, A. 2004. Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints, Math. Program., 99, 329350. Dentcheva, D., Ruszczynski, A. 2009. Optimization with multivariate stochastic dominance constraints", Mathematical Programming 117, 111127. Denuit, M., L.\ Eeckhoudt, B.\ Rey. 2010. Some consequences of correlation aversion in decision science. Annals of Operations Research 176(1), 259269. Egozcue, M., Wong, W.K., 2010. Gains from Diversification: A Majorization and Stochastic Dominance Approach. European Journal of Operational Research 200, 893900. Eisner, R., Strotz, R., 1961. Flight insurance and the theory of choice. Journal of Political Economy 69, 355368. Fong, W.M., Wong, W.K., Lean, H.H., 2005. International Momentum Strategies: A Stochastic Dominance Approach. Journal of Financial Markets 8, 89109. Guo, X., Wong, W.K., 2016. Multivariate Stochastic Dominance for Risk Averters and Risk Seekers, RAIRO  Operations Research, (forthcoming). Hadar, J., Russell, W.R., 1971. Stochastic Dominance and Diversification. Journal of Economic Theory 3, 288305. Hammond, J.S., 1974. Simplifying the Choice between Uncertain Prospects where Preference is Nonlinear. Management Science 20(7), 10471072. Hardy, G.H., Littlewood, J.E., Polya, G., 1934. Inequalities, Cambridge University Press, Cambridge, MA. Hazen, G.B., 1986. Partial information, dominance, and potential optimality in multiattribute utility theory. Operations research 34(2), 296310. Hoang, T.H.V., Wong, W.K., Zhu, Z.Z., 2015. Is gold different for riskaverse and riskseeking investors? An empirical analysis of the Shanghai Gold Exchange, Economic Modelling 50, 200211. HomemdeMello, T., Mehrotra, S. (2009). A cutting surface method for uncertain linear programs with linear stochastic dominance constraints. SIAM J. Optim. 20, 12501273. Hu, J., HomemdeMello, T., Mehrotra, S. (2012). Sample average approximation of stochastic dominance constrained programs. Math. Programming 133, 171201. Jean, W.H., 1980. The geometric mean and stochastic dominance. Journal of Finance 35(1), 151158. Jegadeesh, N., Titman, S., 1993. Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. Journal of Finance 48, 6591. Keeney, R.L., Raiffa, H., 1976. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York. Levy, H., 1973. Stochastic Dominance, Efficiency Criteria, and Efficient Portfolios: The MultiPeriod Case. American Economic Review 43, 986994. Levy H., 1992. Stochastic dominance and expected utility: Survey and analysis. Management Science 38(4), 555593. Li, C.K., Wong, W.K., 1999. Extension of Stochastic Dominance Theory to Random Variables. RAIRO Operations Research 33, 509524. Markowitz, H.M., 1952a. The Utility of Wealth. Journal of Political Economy 60, 151156. Markowitz, H.M., 1952b. Portfolio Selection. Journal of Finance 7, 7791. Ok, E., Kranich, L., 1998. The Measurement of Opportunity Inequality: a CardinalityBased Approach. Social Choice Welfare 15, 263287. Qiao, Z., Clark, E., Wong, W.K., 2012, Investors' Preference towards Risk: Evidence from the Taiwan Stock and Stock Index Futures Markets, Accounting & Finance, DOI: 10.1111/j.1467629X.2012.00508.x. Quirk, J.P., Saposnik, R. 1962. Admissibility and Measurable Utility Functions. Review of Economic Studies 29, 140146. Samuelson, P.A., 1967. General Proof that Diversification Pays. Journal of Financial and Quantitative Analysis 2(1), 113. Sriboonchita, S., Wong, W.K., Dhompongsa, D., Nguyen, H.T., 2009. Stochastic Dominance and Applications to Finance, Risk and Economics. Chapman and Hall/CRC, Boca Raton, Florida. von Neumann, J., Morgenstern, O., 1944. Theory of Games and Economic Behavior. Princeton University Press, Princeton N.J. Wong, W.K., 2007. Stochastic Dominance and MeanVariance Measures of Profit and Loss for Business Planning and Investment. European Journal of Operational Research 182, 829843. Wong, W.K., Chan, R., 2008. Markowitz and Prospect Stochastic Dominances. Annals of Finance 4(1), 105129. Wong, W.K., Li, C.K., 1999. A Note on Convex Stochastic Dominance Theory. Economics Letters 62, 293300. Wong, W.K., Ma, C., 2008. Preferences over LocationScale Family, Economic Theory 37(1), 119146. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/70637 