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On a subjective approach to risk measurement

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  • Piotr Jaworski

Abstract

This study is based on the analogy between hedging a risky asset and keeping reserves to meet an unknown demand. The optimal hedging level, which depends on individual preferences, is regarded as a measure of risk. We determine the set of optimal levels and investigate the properties of the associated risk measures. This approach provides a new insight into Value at Risk (VaR). We consider it as a solution of a certain optimal inventory problem with linear cost and loss functions. We show that these functions determine the confidence level of VaR. In this way we obtain a simple model that helps us to choose a proper confidence level α and explains why supervisory institutions (such as the Basle Committee) choose a higher α than financial institutions themselves.

Suggested Citation

  • Piotr Jaworski, 2006. "On a subjective approach to risk measurement," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 495-511.
    • Handle: RePEc:taf:quantf:v:6:y:2006:i:6:p:495-511
    DOI: 10.1080/14697680600739120
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    References listed on IDEAS

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    1. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
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    6. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    7. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    2. Jaworski, Piotr & Krzywda, Marcin, 2013. "Coupling of Wiener processes by using copulas," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2027-2033.

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