The Monge—Kantorovich problems and stochastic preference relations

  • Vladimir L. Levin
Part of the Advances in Mathematical Economics book series (MATHECON, volume 3)


A method in mathematical utility theory based on the duality theorems for the general Monge—Kantorovich problem proves to be fruitful in various parts of mathematical economics. In the present survey we give further development of that method and study its applications to closed preference relations (resp. correspondences) on a topological space (resp. between two topological spaces) and to their convex stochastic extensions on the corresponding spaces of lotteries. Among other results, we prove characterization theorems:
  • for a functionally closed preorder (Theorem 2.1);

  • for the corresponding strong stochastic dominance (Theorems 2.2 and 3.1);

  • for the convex stochastic extension of an arbitrary closed correspondence between two topological spaces (Theorem 4.1).

Key words

Radon measure Monge-Kantorovich problem functionally closed preorder strong stochastic dominance isotone function utility function closed preference relation closed correspondence 

JEL Classification

C69 D81 

Mathematics Subject Classification (2000)

91B16 28C15 54F05 


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Copyright information

© Springer Japan 2001

Authors and Affiliations

  • Vladimir L. Levin
    • 1
  1. 1.Central Economics and MathematicsInstitute of Russian Academy of SciencesMoscowRussia

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