Definition
Consider a portfolio Then a spectral risk measure where is non-negative, non-increasing, right-continuous, integrable function defined on such that is defined by
where is the cumulative distribution function for X.
If there are equiprobable outcomes with the corresponding payoffs given by the order statistics . Let . The measure defined by is a spectral measure of risk if satisfies the conditions
- Nonnegativity: for all ,
- Normalization: ,
- Monotonicity : is non-increasing, that is if and .
Read more about this topic: Spectral Risk Measure
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