After Fooled by Randomness and The Black Swan, Nassim Taleb comes up with Antifragility (book to be released very soon).
Very briefly, antifragility means that some things may benefit from disorder. Usually we tend to think that things are either fragile or robust. Well, this way of, in a sense, striving for robustness misses the whole point: What we should aim at is antifragility. We should try to gain from noise when possible, in other words shoot for convexity.
In the attached paper, Brice Magdalou (Lameta, University of Montpellier), Richard Nock (Ceregmia, University of French West Indies) and myself draw on information geometry concepts to show that important ideas in Antifragility can be captured into a premium which we call Taleb's premium. This premium is structured around so-called Bregman divergences (which by he way are linked to Jensen's inequality).
You will learn not to trust the Almighty Mean!
One piece of advice: Walk (slowly), muse, gaze and look around you what is or could be antifragile. Believe us, this is time well spent!
Here is the paper.