  We propose a generalization of the classical notion of the $V@R_{\lambda}$
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 $V@R_{\lambda}$ 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 $\mathcal{P}(% \mathbb{R}).$
