Uniformly monotone functions - defiitions, properties, characterizations

Abstract

Quasi-concave functions play an important role in economics and finance as utility functions, measures of risk or other objects used, mainly,in portfolio selection analysis. A special attention is 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 overcome by establishing of uniformly quasi-concave functions, due to Prékopa, Yoda andSubasi (2011). We contribute with a new characterization of uniformlyquasi-concave functions that allows easier verfication and provide morestraightforward insight.