Characterization of uniformly quasi-concave functions

Quasi-concave functions appears in economics and finance as utility functions, measures of risk or other objects, mainly in portfolio selection analysis. A special attention was paid to these functions in the minimax theory. Unfortunately, their limited application is due to the fact that supremum, sum, product of quasi-concave functions are typically not quasi-concave. This difficulty is removed by establishing of uniformly quasi-concave functions, due to Prekopa, Yoda and Subasi (2011). Supremum and sum of uniformly quasi-concave functions are also a quasi-concave function. Moreover, product of nonnegative uniformly quasi-concave functions is a quasi-concave function. We contribute with a new characterization of uniformly quasi-concave functions that allows for easier verification and provide more straightforward insight. Hence, application and usage of uniformly quasi-concave functions become to be easier and more natural.