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$-f''(x)/f'(x)$ is known to economists as the Arrow Pratt measure of absolute risk aversion. We want to use it in a paper to capture a scale invariant notion of concavity while specifcally avoiding any term that suggests we are talking about risk. There is an interesting discussion of this issue in this thread but sadly it doesn't answer my particular question about terminology

Leo Simon
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    Well it's the additive inverse of the logarithmic derivative of the derivative. I don't think that helps you though. – Matt Samuel Feb 13 '18 at 02:14
  • My only suggestion is the obvious one: just define some new symbol to denote this ratio, and refer it to using the symbol. You don't need to give it a name. Just explain that it's a measure of convexity/concavity. – bubba Feb 13 '18 at 08:22
  • Thanks! I do like names, though. Do you think any mathy types would complain about the word "normalized curvature"? – Leo Simon Feb 13 '18 at 15:54
  • I think "normalized curvature" is a bit problematic because it sounds like some sort of curvature measure, which your ratio is not (as far as I can see). How about something more vague, like "derivative ratio", or "convexity ratio", or "convexity coefficient". – bubba Feb 15 '18 at 09:49
  • we like the idea of normalized concavity'' butconcavity coefficient'' would be an alternative if you think that ``normalized'' conveys the wrong idea – Leo Simon Feb 15 '18 at 14:00

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