Risk measures

$We$ defined the VaR $of$ a portfolio with time $t$ value $of{V}_{t}as{V}_0-F^{-1}(1-p)$ and the

PFE $of$ the portfolio $as{F}^{-1}(p),$ where $F(x)is$ the $CDFof$ the future portfolio values:

$F(x)=P[V_{t}x]=E^P[1_{V_t}x]$

Sometimes the VaR $is$ expressed $as{G}^{-1}(p),$ where $G(x)is$ the probability that the losses

are less than $x$ :

$FGGxG(x)=P[V_0-V_{t}x]$