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
Famous quotes containing the word definition:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)