# Tag Info

Translation invariance of a risk measure $\rho$ is defined as $$\rho(X+k) = \rho(X)-k,$$ where $X$ is a random variable such that $\rho(X)$ exists and $k$ is a constant. The meaning is that if I add an amount $k$ to my risky positions then the risk is reduced by this amount. For VaR we consider the case that $X$ has a continuous distribution and that it ...