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Capital Allocation And Risk Contribution With Discrete‐Time Coherent Risk

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  • Alexander S. Cherny

Abstract

We define the capital allocation and the risk contribution for discrete‐time coherent risk measures and provide several equivalent representations of these objects. The formulations and the proofs are based on two instruments introduced in the paper: a probabilistic notion of the extreme system and a geometric notion of the generator. These notions are also of interest on their own and are important for other applications of coherent risk measures. All the concepts and results are illustrated by JP Morgan's Risk Metrics model.

Suggested Citation

  • Alexander S. Cherny, 2009. "Capital Allocation And Risk Contribution With Discrete‐Time Coherent Risk," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 13-40, January.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:1:p:13-40
    DOI: 10.1111/j.1467-9965.2008.00355.x
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    References listed on IDEAS

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    Cited by:

    1. Guangyan Jia & Mengjin Zhao, 2022. "On the Correspondence and the Risk Contribution for Conditional Coherent and Deviation Risk Measures," Papers 2208.13336, arXiv.org, revised Feb 2023.
    2. 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.
    3. 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.
    4. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2016. "A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective," Papers 1603.09030, arXiv.org, revised Jan 2017.
    5. Tomasz R. Bielecki & Igor Cialenco & Shibi Feng, 2018. "A Dynamic Model of Central Counterparty Risk," Papers 1803.02012, arXiv.org.
    6. 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.
    7. Alejandro Ferrer Pérez & José Casals Carro & Sonia Sotoca López, 2014. "Linking the problems of estimating and allocating unconditional capital," Documentos de Trabajo del ICAE 2014-13, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    8. D. Madan & M. Pistorius & M. Stadje, 2017. "On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation," Finance and Stochastics, Springer, vol. 21(4), pages 1073-1102, October.
    9. Cossette, Hélène & Marceau, Etienne & Trufin, Julien & Zuyderhoff, Pierre, 2020. "Ruin-based risk measures in discrete-time risk models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 246-261.
    10. Tomasz R. Bielecki & Igor Cialenco & Shibi Feng, 2018. "A Dynamic Model Of Central Counterparty Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-34, December.

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