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Multivariate risk measures in the non-convex setting

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  • Andreas Haier
  • Ilya Molchanov

Abstract

The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite number of transfers are possible. The paper presents an approach to measure risks of such positions based on the idea of considering all selections of the portfolio and checking if one of them is acceptable. Properties and basic examples of risk measures of non-convex portfolios are presented.

Suggested Citation

  • Andreas Haier & Ilya Molchanov, 2019. "Multivariate risk measures in the non-convex setting," Papers 1902.00766, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1902.00766
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    File URL: http://arxiv.org/pdf/1902.00766
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    References listed on IDEAS

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    1. M. Kaina & L. Rüschendorf, 2009. "On convex risk measures on L p -spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 475-495, July.
    2. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    3. Ilya Molchanov & Ignacio Cascos, 2016. "Multivariate Risk Measures: A Constructive Approach Based On Selections," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 867-900, October.
    4. Emmanuel Lepinette & Ilya Molchanov, 2017. "Conditional cores and conditional convex hulls of random sets," Papers 1711.10303, arXiv.org.
    5. repec:dau:papers:123456789/342 is not listed on IDEAS
    6. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    7. Andreas Haier & Ilya Molchanov & Michael Schmutz, 2015. "Intragroup transfers, intragroup diversification and their risk assessment," Papers 1511.06320, arXiv.org, revised Nov 2016.
    8. Andreas Haier & Ilya Molchanov & Michael Schmutz, 2016. "Intragroup transfers, intragroup diversification and their risk assessment," Annals of Finance, Springer, vol. 12(3), pages 363-392, December.
    9. Ignacio Cascos & Ilya Molchanov, 2013. "Multivariate risk measures: a constructive approach based on selections," Papers 1301.1496, arXiv.org, revised Jul 2016.
    10. Johannes Leitner, 2004. "Balayage Monotonous Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(07), pages 887-900.
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    Cited by:

    1. Antonio Avilés López & José Miguel Zapata García, 2020. "Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations," Mathematics, MDPI, vol. 8(10), pages 1-23, October.

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