Talk:Coherent risk measure

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[edit] Incohorent 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.

Joaquin

[edit] Third rule

I don't understand the third rule, translational invariance. What is d?

Shouldn't the fourth rule be called 'linearity' not 'homogeneity'?

[edit] Clarification of rho, X, and Y

The monotonicity axiom is confusing if you don't know what ρ represents. Is ρ an antitone function? Seems to me that if X and Y represent the value of a risky item, and ρ is a risk-quantification measure, then monotonicity should be:
if X \leq Y then \rho(X) \leq \rho(Y)
That is, a highly priced item is considered riskier (note the reversal of the implication as well).
--203.185.215.144 23:44, 28 February 2007 (UTC) Greg

With X andY representing (future) values of a risky portfolio, the monotonicity axiom is exactly the opposite:
if X \geq Y then \rho(X) \leq \rho(Y),
meaning if X portfolio value is higher than Y portfolio value for every possible outcome (state of the world), then its risk (identified with the cash amount that has to be added to the portfolio to become acceptable) should be smaller. Just check Artzner et al. I will correct this if nobody has any objections. -- Zsolt Tulassay 15:09, 15 June 2007 (UTC)