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Complete Monotone Quasiconcave Duality

Author

Listed:
  • Simone Cerreia-Vioglio
  • Fabio Maccheroni
  • Massimo Marinacci
  • Luigi Montrucchio

Abstract

We introduce a notion of complete monotone quasiconcave duality and we show that it holds for important classes of quasiconcave functions.

Suggested Citation

  • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Complete Monotone Quasiconcave Duality," Carlo Alberto Notebooks 80, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:80
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    References listed on IDEAS

    as
    1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Risk Measures: Rationality and Diversification," Carlo Alberto Notebooks 100, Collegio Carlo Alberto.
    2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    3. Newman, Peter, 1969. "Some properties of concave functions," Journal of Economic Theory, Elsevier, vol. 1(3), pages 291-314, October.
    4. J. P. Crouzeix, 1980. "Conditions for Convexity of Quasiconvex Functions," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 120-125, February.
    5. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    6. Jean-Paul Penot & Michel Volle, 1990. "On Quasi-Convex Duality," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 597-625, November.
    7. Massimo Marinacci & Luigi Montrucchio, 2006. "On Concavity and Supermodularity," Carlo Alberto Notebooks 5, Collegio Carlo Alberto.
    8. Martinez-Legaz, J. -E., 1991. "Duality between direct and indirect utility functions under minimal hypotheses," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 199-209.
    9. Crouzeix, J. -P., 1983. "Duality between direct and indirect utility functions : Differentiability properties," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 149-165, October.
    10. Diewert, W.E., 1993. "Duality approaches to microeconomic theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 12, pages 535-599, Elsevier.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Youichiro Higashi & Kazuya Hyogo & Norio Takeoka, 2020. "Costly Subjective Learning," KIER Working Papers 1040, Kyoto University, Institute of Economic Research.
    2. ,, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    3. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "On the equality of Clarke-Rockafellar and Greenberg-Pierskalla differentials for monotone and quasiconcave functionals," Working Papers 561, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    5. Sigrid Kallblad, 2013. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Papers 1311.7419, arXiv.org.
    6. Marco Frittelli & Marco Maggis, 2010. "Dual Representation of Quasiconvex Conditional Maps," Papers 1001.3644, arXiv.org, revised Jan 2010.
    7. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2016. "Absolute and Relative Ambiguity Aversion: A Preferential Approach," Working Papers 578, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    9. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    10. Marco Frittelli & Marco Maggis, 2012. "Complete duality for quasiconvex dynamic risk measures on modules of the $L^{p}$-type," Papers 1201.1788, arXiv.org, revised Sep 2012.
    11. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2012. "Niveloids and Their Extensions:Risk Measures on Small Domains," Working Papers 458, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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    More about this item

    Keywords

    Quasiconcavity; Quasiconvexity; Duality; Indirect Utility;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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