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Conditional Certainty Equivalent



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


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


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

    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,
    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,, revised Feb 2020.
    7. Alessandro Calvia & Emanuela Rosazza Gianin, 2019. "Risk measures and progressive enlargement of filtration: a BSDE approach," Papers 1904.13257,, revised Mar 2020.


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