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Smooth feasible solutions to a dual Monge–Kantorovich problem with applications to best approximation and utility theory in mathematical economics

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Advances in Mathematical Economics

Part of the book series: Advance in Mathematical Economics ((MATHECON,volume 12))

Abstract

Given a (closed or open) subset X in Rn, which is stable with respect to shifts in positive directions, weconsider inequalities u(x) – u(y) ≤c(x,y),x,y ∈ X, and for a wide class of functions c on X × X, derive a smooth solution to these inequal ities from a Lebesgue measurable one. Applications are given to a best approximation problem and to several problems of mathematical economics relating to preferences that admit smooth (or Lipschitz continuous) utility functions, smooth-utility-rational choice, and smooth representations of interval orders.

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Authors and Affiliations

  1. Central Economics and Mathematics Institute of the Russian Academy of Sciences, Nakhimovskii Prospect 47, Moscow, 117418, Russia

    Vladimir L. Levin

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  1. Vladimir L. Levin
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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku Tokyo, 153-0041, Japan

    S. Kusuoka

  2. Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

    T. Maruyama

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Levin, V.L. (2009). Smooth feasible solutions to a dual Monge–Kantorovich problem with applications to best approximation and utility theory in mathematical economics. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advance in Mathematical Economics, vol 12. Springer, Tokyo. https://doi.org/10.1007/978-4-431-92935-2_4

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