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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. 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. Massimo Marinacci & Luigi Montrucchio, 2006. "On Concavity and Supermodularity," Carlo Alberto Notebooks 5, Collegio Carlo Alberto.
    6. 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.
    7. 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.
    8. 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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. 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.
    2. Marco Frittelli & Marco Maggis, 2010. "Dual Representation of Quasiconvex Conditional Maps," Papers 1001.3644, arXiv.org, revised Jan 2010.
    3. 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.
    4. Cerreia-Vioglio, Simone, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    5. 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.
    6. 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.
    7. Sigrid Källblad, 2017. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Finance and Stochastics, Springer, vol. 21(2), pages 397-425, April.
    8. Sigrid Kallblad, 2013. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Papers 1311.7419, arXiv.org.
    9. 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.
    10. repec:eee:ejores:v:267:y:2018:i:1:p:200-211 is not listed on IDEAS

    More about this item

    Keywords

    Quasiconcavity; Quasiconvexity; Duality; Indirect Utility;

    JEL classification:

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

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