Talk:Coherent risk measure
The page gives no clue what X and Y are.
The reader wants to assume these are securities or investments, so that \rho(X) is the risk of X. But then we have:
"Monotonicity
\rho(X) \leq \rho(Y) whenever Y \leq X "
So X can't be an investment: one investment is not less than another. Unless we have some ordering of investments which is not explained and is totally mysterious. Nor can X be the value of a particular investment, since the risk of an investment (if \rho is indeed risk) is not a function of the value of that investment.
This article might make sense to someone who is familiar with the broader subject matter, serving to remind them of something they already know, or providing details about something they understand generally.
But it offers nothing but confusion and mystery to the non-expert reader who wants to know what a coherent risk measure is.
I don't understand the third rule, translational invariance. What is d?
Shouldn't the fourth rule be called 'linearity' not 'homogeneity'?