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Conditional divergence risk measures

Author

Listed:
  • Giulio Principi
  • Fabio Maccheroni

Abstract

Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures. In particular, we study the conditional counterpart of optimized certainty equivalents. In the process, we provide representation results for niveloids in the conditional $L^{\infty}$-space. By employing such representation results we retrieve a conditional version of the variational formula for optimized certainty equivalents. In conclusion, we apply this formula to provide a variational representation of the conditional entropic risk measure.

Suggested Citation

  • Giulio Principi & Fabio Maccheroni, 2022. "Conditional divergence risk measures," Papers 2211.04592, arXiv.org.
    • Handle: RePEc:arx:papers:2211.04592
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    File URL: http://arxiv.org/pdf/2211.04592
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    References listed on IDEAS

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    3. Aharon Ben-Tal & Marc Teboulle, 1986. "Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming," Management Science, INFORMS, vol. 32(11), pages 1445-1466, November.
    4. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    5. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
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