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Stochastic Dominance

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  • Ricard Torres

Abstract

We develop in this paper a systematic study of the stochastic dominance ordering in spaces of measures. We collect and present in an orderly fashion, results that are spread out in the Applied Probability and Mathematical Economics literature, and extend most of them to a somewhat broader framework. Several original contributions are made on the way. We provide a sharp characterization of conditions that permit an equivalent definition of stochastic dominance by means of continuous and monotone functions. When the preorder of the original space is closed, we offer an extremely simple equivalent characterization of stochastic dominance, a result of which we have found no parallel in literature. We develop original methods that shed light into the inheritance of the antisymmetric property by the stochastic dominance ordering. We study how the topological properties of the preorder translate to the stochastic dominance preorder. A class of spaces in which monotone and continuous functions are convergence-determining is described. Finally, conditions are given that guarantee that (order) bounded stochastically monotone nets, have a limit point.We develop in this paper a systematic study of the stochastic dominance ordering in spaces of measures. We collect and present in an orderly fashion, results that are spread out in the Applied Probability and Mathematical Economics literature, and extend most of them to a somewhat broader framework. Several original contributions are made on the way. We provide a sharp characterization of conditions that permit an equivalent definition of stochastic dominance by means of continuous and monotone functions. When the preorder of the original space is closed, we offer an extremely simple equivalent characterization of stochastic dominance, a result of which we have found no parallel in literature. We develop original methods that shed light into the inheritance of the antisymmetric property by the stochastic dominance ordering. We study how the topological properties of the preorder translate to the stochastic dominance preorder. A class of spaces in which monotone and continuous functions are convergence-determining is described. Finally, conditions are given that guarantee that (order) bounded stochastically monotone nets, have a limit point.

Suggested Citation

  • Ricard Torres, 1990. "Stochastic Dominance," Discussion Papers 905, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:905
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    Cited by:

    1. Cuong Van & John Stachurski, 2007. "Parametric continuity of stationary distributions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 333-348, November.
    2. Gong, Liutang & Zhao, Xiaojun & Yang, Yunhong & Hengfu, Zou, 2010. "Stochastic growth with social-status concern: The existence of a unique stable distribution," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 505-518, July.
    3. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    4. Takashi Kamihigashi & John Stachurski, 2009. "Asymptotics Of Stochastic Recursive Economies Under Monotonicity," KIER Working Papers 666, Kyoto University, Institute of Economic Research.

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