We propose a generalization of the classical notion of the V @R that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by de ning a new class of law invariant risk measures based on an appropriate family of acceptance sets. The V @R and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on P(R):
Frittelli, M., Maggis, M., Peri, I. (2012). Risk Measures on P(R) and Value At Risk with Probability/Loss function [Working paper del dipartimento].
Risk Measures on P(R) and Value At Risk with Probability/Loss function
PERI, ILARIA
2012
Abstract
We propose a generalization of the classical notion of the V @R that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by de ning a new class of law invariant risk measures based on an appropriate family of acceptance sets. The V @R and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on P(R):
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