Talk:Coherent risk measure

message: ; Monotonicity
: \mathrm{If}\; Z_1,Z_2 \in \mathcal{L} \;\mathrm{and}\; Z_1 \leq Z_2 ,\; \mathrm{then} \; \rho(Z_1) \leq \rho(Z_2) 
That is, if portfolio Z_2 has better values than portfolio Z_1 under all scenarios then the risk of Z_2 should be bigger than the risk of Z_1: more profit, more risk.Wilmott P. (2006) Quantitative Finance, Wiley, 2nd. Ed., Vol. 1, p. 342.
That is wrong. If all scenarios are worse the risk measure should be higher, not lower, as stated. See for that: http://www.math.ethz.ch/~delbaen/ftp/preprints/CoherentMF.pdf page 7  —Preceding unsigned comment added by 91.34.52.136 (talk) 13:58, 29 March 2010 (UTC)
thread_title:  Monotonicity 

message: Could someone add an example illustrating this as it's not immediately obvious. An example would be of great benefit in my opinion  —Preceding unsigned comment added by Red.devil.ade (talk • contribs) 09:30, 18 February 2009 (UTC)
thread_title:  Non-coherance of VaR 

message: Shouldn't it be +a instead of -a after the equality? Like this:
; Translation invariance
: \mathrm{If}\; a \in \mathbb{R} \; \mathrm{and} \; Z \in \mathcal{L} ,\;\mathrm{then}\; \rho(Z + a) = \rho(Z) + a 
For instance top page 7 in this article suggests the same:
http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.3340v1.pdf
Or am I wrong?  —Preceding unsigned comment added by MVjensen (talk • contribs) 11:02, 12 November 2009 (UTC)
thread_title:  Translation invariance, which sign? 

message: There are many other risk measures that are not cohrent (eg. VAR, standard deviation, etc.).
Ok to write a small text about them too?
Phdb (talk) 14:22, 12 August 2011 (UTC)
replies: text:  I think a small text about them would be ok, though it should more be just to comment that other types of risk measures exist.  I would not suggest using standard deviation (or variance) since they are not actually risk measures. Zfeinst (talk) 17:34, 12 August 2011 (UTC)
thread_title: Other non-coherent measures than VaR

message: In external links there is the page
: Glyn Holton: The Case for Incoherence 
given.  I just read this blog post and the initial example is misinterpreted (which gives rise, I feel, to an incorrect conclusion).  I would propose removing this link for this reason.
The example (from the post) to which I am referring states: There are three wells, one or more of which may be poisoned.  Should you drink from just one well or from all three?  
In the post, it argues of course you drink from just 1; I agree.  However, the author (Glyn Holton) goes from this to stating that subadditivity was violated, which is incorrect.  Subadditivity would say
: \rho(\text{drink from all 3}) \leq \sum_{i = 1}^3 \rho(\text{drink from well }i)
which can trivially be satisfied by situations where \rho(\text{drink from well }i) < \rho(\text{drink from all 3}) for all wells.  In fact, the "return" of drinking from all 3 wells is worse than the "return" of drinking from just 1 well with probability 1 (death certain unless all wells clean vs. death certain only in subset of those cases).  Therefore by monotonicity we have that \rho(\text{drink from well }i) \leq \rho(\text{drink from all 3}) for all wells.
Am I missing something? Does anyone object to removing the link? Thanks. Zfeinst (talk) 04:06, 12 March 2012 (UTC)
thread_title:  External link: The Case for Incoherence