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.
Recall:
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The median is the value separating the upper and lower halves of a data set or of a probability distribution.
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The mode represents the most frequent value in a data set. The notion is transferable to a probability distribution.
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- 2.
- 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.
The term portfolio is here used stricto sensus and not necessarily as a combination of assets.
- 5.
All these distributions will be used in different ways in our application.
- 6.
Ξ represents the set of all probability measures on ( Ω, P) which are absolutely continuous with respect to P.
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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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