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Conditional Certainty Equivalent

Author

Listed:
  • MARCO FRITTELLI

    () (Department of Mathematics, University of Milan, via C. Saldini 50 Milan, 20134, Italy)

  • MARCO MAGGIS

    () (Department of Mathematics, University of Milan, via C. Saldini 50 Milan, 20134, Italy)

Abstract

In a dynamic framework, we study the conditional version of the classical notion of certainty equivalent when the preferences are described by a stochastic dynamic utility u(x,t,ω). We introduce an appropriate mathematical setting, namely Orlicz spaces determined by the underlying preferences and thus provide a systematic method to go beyond the case of bounded random variables. Finally we prove a conditional version of the dual representation which is a crucial prerequisite for discussing the dynamics of certainty equivalents.

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:n:s0219024911006255
    DOI: 10.1142/S0219024911006255
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    References listed on IDEAS

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    1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Risk Measures: Rationality and Diversification," Carlo Alberto Notebooks 100, Collegio Carlo Alberto.
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    Cited by:

    1. Massoomeh Rahsepar & Foivos Xanthos, 2020. "On the extension property of dilatation monotone risk measures," Papers 2002.11865, arXiv.org.
    2. Centrone, Francesca & Rosazza Gianin, Emanuela, 2018. "Capital allocation à la Aumann–Shapley for non-differentiable risk measures," European Journal of Operational Research, Elsevier, vol. 267(2), pages 667-675.
    3. Asgar Jamneshan & Michael Kupper & José Miguel Zapata-García, 0. "Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time," Journal of Optimization Theory and Applications, Springer, vol. 0, pages 1-23.
    4. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2015. "Portfolio Optimization with Quasiconvex Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1042-1059, October.
    5. Asgar Jamneshan & Michael Kupper & José Miguel Zapata-García, 2020. "Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 644-666, August.
    6. Marco Maggis & Andrea Maran, 2018. "Stochastic Dynamic Utilities and Inter-Temporal Preferences," Papers 1803.05244, arXiv.org, revised Feb 2020.
    7. Alessandro Calvia & Emanuela Rosazza Gianin, 2019. "Risk measures and progressive enlargement of filtration: a BSDE approach," Papers 1904.13257, arXiv.org, revised Mar 2020.

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