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 defining 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 defined on the entire set of distribution functions. JOINT with Marco Maggis e Ilaria Peri. Il seminario si terrà presso la sala grande di Prometeia (primo piano accesso da via Marconi).