A coherent risk measure is:
$\rho(\lambda X_1+(1-\lambda X_2))$
How can it be shown that everey convex risk measure is indeed a coherent risk measure?
I assume that it is enough to show that a convex risk measure is coherent by using, subadditivity, positive homogeniety. So we get: $\rho(\lambda X_1+(1-\lambda X_2))=\rho(\lambda X_1)+\rho((1-\lambda)X_2)=\lambda \rho(X_1)+(1-\lambda)\rho(X_2))$ right?