Risk Measures on P(R) and value at risk with probability/loss function

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 deÖning 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).