Uniformly monotone functions - Definition, properties, characterizations

Quasi-concave functions play an important role in economics and finance as utility functions, measures of risk or the other objects used, mainly, in portfolio selection analysis. Unfortunately, their limited application is due to the fact that their supremum, sum, product are typically not quasi-concave. This difficulty is overcome by establishing uniformly quasi-concave functions. We contribute with a new characterization of uniformly quasi-concave functions that allows easier verification and provide more straightforward insight.