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Measuring risk with multiple eligible assets

Author

Listed:
  • Walter Farkas
  • Pablo Koch-Medina
  • Cosimo Munari

Abstract

The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and continuity properties of these risk measures with respect to multiple eligible assets. Our finiteness and continuity results highlight the interplay between the acceptance set and the class of eligible portfolios. We present a simple, alternative approach to the dual representation of convex risk measures by directly applying to the acceptance set the external characterization of closed, convex sets. We prove that risk measures are nondegenerate if and only if the pricing functional admits a positive extension which is a supporting functional for the underlying acceptance set, and provide a characterization of when such extensions exist. Finally, we discuss applications to set-valued risk measures, superhedging with shortfall risk, and optimal risk sharing.

Suggested Citation

  • Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2013. "Measuring risk with multiple eligible assets," Papers 1308.3331, arXiv.org, revised Mar 2014.
    • Handle: RePEc:arx:papers:1308.3331
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    References listed on IDEAS

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    3. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
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    9. repec:bla:ecnote:v:33:y:2004:i:3:p:415-435 is not listed on IDEAS
    10. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    11. repec:arz:wpaper:eres1993-121 is not listed on IDEAS
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    Cited by:

    1. Zachary Feinstein & Birgit Rudloff, 2018. "Time consistency for scalar multivariate risk measures," Papers 1810.04978, arXiv.org, revised Nov 2021.
    2. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    3. Koch-Medina Pablo & Munari Cosimo, 2014. "Law-invariant risk measures: Extension properties and qualitative robustness," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 215-236, December.
    4. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Munari, Cosimo, 2015. "Capital adequacy tests and limited liability of financial institutions," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 93-102.

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