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Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type

Author

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  • Frittelli Marco

    (Dipartimento di Matematica, Università degli Studi di Milano)

  • Maggis Marco

    (Dipartimento di Matematica Università degli Studi di Milano)

Abstract

In the conditional setting we provide a complete duality between quasiconvex risk measures defined on L0 modules of the Lp type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued maps.

Suggested Citation

  • Frittelli Marco & Maggis Marco, 2014. "Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 1-26, March.
    • Handle: RePEc:bpj:strimo:v:31:y:2014:i:1:p:26:n:3
    DOI: 10.1515/strm-2013-1163
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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. Tiexin Guo, 2010. "Recent progress in random metric theory and its applications to conditional risk measures," Papers 1006.0697, arXiv.org, revised Mar 2011.
    3. Marco Frittelli & Marco Maggis, 2011. "Conditional Certainty Equivalent," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 41-59.
    4. Jean-Paul Penot & Michel Volle, 1990. "On Quasi-Convex Duality," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 597-625, November.
    5. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    6. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    7. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
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    Cited by:

    1. c{C}au{g}{i}n Ararat & Mucahit Aygun, 2021. "Dual representations of quasiconvex compositions with applications to systemic risk," Papers 2108.12910, arXiv.org.

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