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The Traditional Risk Measures

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Risk Measurement

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Abstract

Traditional literature enumerates risk measures without any attempt to classify them. Nevertheless several taxonomies can be used to distinguish between them.

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Notes

  1. 1.

    Recall:

    • The median is the value separating the upper and lower halves of a data set or of a probability distribution.

    • The mode represents the most frequent value in a data set. The notion is transferable to a probability distribution.

  2. 2.

    http://www.ruf.rice.edu/%7Elane/.

  3. 3.

    The proposition in probability theory known as the law of total expectation or the tower rule states that if X is a random variable whose expected value E(X) is defined, and Y  is any random variable on the same probability space, then

    $$\displaystyle \begin{aligned} E(X) = E(E(X\mid Y)). \end{aligned} $$
    (3.1.33)
  4. 4.

    The term portfolio is here used stricto sensus and not necessarily as a combination of assets.

  5. 5.

    All these distributions will be used in different ways in our application.

  6. 6.

    Ξ represents the set of all probability measures on ( Ω, P) which are absolutely continuous with respect to P.

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Author information

Authors and Affiliations

  1. LabEx ReFi and IPAG, University Paris1 Panthéon-Sorbonne, Paris, France

    Dominique Guégan

  2. University Ca’Foscari, Venezia, Italy

    Dominique Guégan

  3. Department of Computer Science, University College London, London, UK

    Bertrand K. Hassani

  4. Department of Finance, Université Paris 1 Panthéon-Sorbonne, Paris, France

    Bertrand K. Hassani

  5. Department of Financial Regulation, LabeX Refi (ESCP - ENA - Paris 1), Paris, France

    Bertrand K. Hassani

Authors
  1. Dominique Guégan
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  2. Bertrand K. Hassani
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Guégan, D., Hassani, B.K. (2019). The Traditional Risk Measures. In: Risk Measurement. Springer, Cham. https://doi.org/10.1007/978-3-030-02680-6_3

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