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DIFFERENTIABILITY OF BSVIEs AND DYNAMIC CAPITAL ALLOCATIONS

Author

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  • EDUARD KROMER

    (Department of Mathematics, University of Gießen, Gießen 35392, Germany)

  • LUDGER OVERBECK

    (Department of Mathematics, University of Gießen, Gießen 35392, Germany)

Abstract

Capital allocations have been studied in conjunction with static risk measures in various papers. The dynamic case has been studied only in a discrete-time setting. We address the problem of allocating risk capital to subportfolios for the first time in a continuous-time dynamic context. For this purpose, we introduce a differentiability result for backward stochastic Volterra integral equations and apply this result to derive continuous-time dynamic capital allocations. Moreover, we study a dynamic capital allocation principle that is based on backward stochastic differential equations and derive the dynamic gradient allocation for the dynamic entropic risk measure.

Suggested Citation

  • Eduard Kromer & Ludger Overbeck, 2017. "DIFFERENTIABILITY OF BSVIEs AND DYNAMIC CAPITAL ALLOCATIONS," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:07:n:s0219024917500479
    DOI: 10.1142/S0219024917500479
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    References listed on IDEAS

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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. Wang, Tianxiao & Yong, Jiongmin, 2019. "Backward stochastic Volterra integral equations—Representation of adapted solutions," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4926-4964.

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