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Dual Representation of Quasiconvex Conditional Maps

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  • Marco Frittelli
  • Marco Maggis

Abstract

We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.

Suggested Citation

  • Marco Frittelli & Marco Maggis, 2010. "Dual Representation of Quasiconvex Conditional Maps," Papers 1001.3644, arXiv.org, revised Jan 2010.
    • Handle: RePEc:arx:papers:1001.3644
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    References listed on IDEAS

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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Risk Measures: Rationality and Diversification," Carlo Alberto Notebooks 100, Collegio Carlo Alberto.
    3. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Complete Monotone Quasiconcave Duality," Carlo Alberto Notebooks 80, Collegio Carlo Alberto.
    4. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    5. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    6. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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