I know this question is sort of dated, but it is something I am currently interested in. 

A very good paper on the topic of convex loss functions and classifier consistency is "[Statistical Behavior and Consistency of Classification Methods Based on Convex Risk Minimization][1]" by Tong Zhang.


  [1]: https://projecteuclid.org/journals/annals-of-statistics/volume-32/issue-1/Statistical-behavior-and-consistency-of-classification-methods-based-on-convex/10.1214/aos/1079120130.full