Talk:Spectral risk measure

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I have corrected the formula for translation invariance, as the sign was previously incorrect.

p(X+a) = p(X)+a — Preceding unsigned comment added by 2A02:C7F:2810:A500:3C1A:9B65:BE5C:454D (talk) 21:35, 2 October 2016 (UTC)[reply]

Since the page is written with

X

as profit/gains the sign was correct. If

X

were to denote the losses then your correction is warranted. In the literature both are used. Zfeinst (talk) 02:47, 3 October 2016 (UTC)[reply]

Hi - I consulted http://press.princeton.edu/titles/10496.html, it uses the positive. (and using the example of Expected Shortfall backs this up) - suggest to change the article to highlight that there is some contention on signage but it doesn't alter the principle? — Preceding unsigned comment added by 2A02:C7F:2810:A500:BC7D:16AF:9ADE:5DDF (talk) 19:55, 4 October 2016 (UTC)[reply]

(Apologies, edit and previous comment are by me, have now created an account!) Lewis Lfogden (talk) 20:05, 4 October 2016 (UTC)[reply]

As long as we are consistent in the article either sign is fine it just should be:

Input is profit/gains with the negative sign for translation-invariance; or
Input is losses with the positive sign.

Of course mathematically the profit is the negative of losses, and that is why you get that negative/positive switch. I am adding a sentence to the article now to indicate that if losses were taken as the input instead then translation-invariance would have a swapped sign. I don't think any other properties would be affected. Zfeinst (talk) 23:31, 4 October 2016 (UTC)[reply]