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Representation Of Bsde-Based Dynamic Risk Measures And Dynamic Capital Allocations

Author

Listed:
  • EDUARD KROMER

    (Department of Mathematics, University of Gießen, Gießen 35390, Germany)

  • LUDGER OVERBECK

    (Department of Mathematics, University of Gießen, Gießen 35390, Germany)

Abstract

In this paper, we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations (BSDEs). We derive this representation from a classical differentiability result for BSDEs and the full allocation property of the Aumann–Shapley allocation. The representation covers BSDE-based dynamic convex and dynamic coherent risk measures. The results are applied to derive a representation for the dynamic entropic risk measure. Our results are also applicable in a specific way to the static case, where we are able to derive a new representation result for static convex risk measures that are Gâteaux-differentiable.

Suggested Citation

  • Eduard Kromer & Ludger Overbeck, 2014. "Representation Of Bsde-Based Dynamic Risk Measures And Dynamic Capital Allocations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-16.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:05:n:s0219024914500320
    DOI: 10.1142/S0219024914500320
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    Citations

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    Cited by:

    1. Silvana M. Pesenti & Sebastian Jaimungal & Yuri F. Saporito & Rodrigo S. Targino, 2023. "Risk Budgeting Allocation for Dynamic Risk Measures," Papers 2305.11319, arXiv.org, revised Oct 2024.
    2. Lesedi Mabitsela & Calisto Guambe & Rodwell Kufakunesu, 2018. "A note on representation of BSDE-based dynamic risk measures and dynamic capital allocations," Papers 1808.04611, arXiv.org.
    3. 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.
    4. Roger J. A. Laeven & Emanuela Rosazza Gianin & Marco Zullino, 2023. "Dynamic Return and Star-Shaped Risk Measures via BSDEs," Papers 2307.03447, arXiv.org, revised Jul 2023.

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