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Fear of loss, inframodularity, and transfers

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  • Müller, Alfred
  • Scarsini, Marco

Abstract

There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity. Inframodular transfers are defined and it is shown that a finite lottery is preferred to another by all expected utility maximizers with an inframodular utility if and only if the first lottery can be obtained from the second via a sequence of inframodular transfers. This result is a natural multivariate generalization of Rothschild and Stiglitzʼs construction based on mean preserving spreads.

Suggested Citation

  • Müller, Alfred & Scarsini, Marco, 2012. "Fear of loss, inframodularity, and transfers," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1490-1500.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1490-1500
    DOI: 10.1016/j.jet.2011.02.002
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    References listed on IDEAS

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    Cited by:

    1. Magdalou, Brice, 2021. "A model of social welfare improving transfers," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    3. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    4. Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2017. "Multidimensional Pigou–Dalton transfers and social evaluation functions," Theory and Decision, Springer, vol. 83(4), pages 573-590, December.
    5. Veli Safak, 2020. "Comparative Statics in Multicriteria Search Models," Papers 2006.14452, arXiv.org.
    6. Kobus, Martyna & Kurek, Radosław, 2018. "Copula-based measurement of interdependence for discrete distributions," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 27-39.
    7. Aouani, Zaier & Chateauneuf, Alain, 2020. "Multidimensional inequality and inframodular order," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 74-79.
    8. Alain Chateauneuf & Bernard Cornet, 2022. "Submodular financial markets with frictions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 721-744, April.
    9. Frank A Cowell & Martyna Kobus & Radoslaw Kurek, 2017. "Welfare and Inequality Comparisons for Uni- and Multi-dimensional Distributions of Ordinal Data," STICERD - Public Economics Programme Discussion Papers 31, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Ceparano, Maria Carmela & Quartieri, Federico, 2017. "Nash equilibrium uniqueness in nice games with isotone best replies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 154-165.
    11. Louis Eeckhoudt & Elisa Pagani & Eugenio Peluso, 2023. "Multidimensional risk aversion: the cardinal sin," Annals of Operations Research, Springer, vol. 320(1), pages 15-31, January.
    12. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2021. "Ranking distributions of an ordinal variable," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 33-80, February.
    13. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    14. Henry Chiu, W., 2020. "Financial risk taking in the presence of correlated non-financial background risk," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 167-179.
    15. Veli Safak, 2020. "Matching Multidimensional Types: Theory and Application," Papers 2006.14243, arXiv.org.
    16. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.

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    More about this item

    Keywords

    Mean preserving spread; Integral stochastic orders; Risk aversion; Ultramodularity; Dual cones;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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