Geodesic
Multivariate stochastic dominance for risk averters and risk seekers
Guo, Xu1, 2 ; Wong, Wing-Keung3, 4, 5 
1 School of Statistics, Beijing Normal University, Beijing, P.R. China.
2 College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China.
3 Department of Finance, Asia University, Taiwan.
4 Faculty of Economics, Hong Kong Baptist University, Hong Kong, P.R. China.
5 Department of Economics, Lingnan University, Hong Kong, P.R. China.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 3, pp. 575-586 Cet article a éte moissonné depuis la source Numdam

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This paper first extends some well-known 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 expected-utility maximization for both risk averters and risk seekers, respectively. 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 non-negative 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.

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DOI : 10.1051/ro/2016026
Classification : D81, G11
Keywords: Multivariate stochastic dominance, risk averters, risk seekers, ascending stochastic dominance, descending stochastic dominance, utility function

Guo, Xu 1, 2 ; Wong, Wing-Keung 3, 4, 5

1 School of Statistics, Beijing Normal University, Beijing, P.R. China.
2 College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China.
3 Department of Finance, Asia University, Taiwan.
4 Faculty of Economics, Hong Kong Baptist University, Hong Kong, P.R. China.
5 Department of Economics, Lingnan University, Hong Kong, P.R. China. 
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     author = {Guo, Xu and Wong, Wing-Keung},
     title = {Multivariate stochastic dominance for risk averters and risk seekers},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {575--586},
     year = {2016},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {3},
     doi = {10.1051/ro/2016026},
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     zbl = {1390.91104},
     language = {en},
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Guo, Xu; Wong, Wing-Keung. Multivariate stochastic dominance for risk averters and risk seekers. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 3, pp. 575-586. doi: 10.1051/ro/2016026

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