Comparison of risk averse utility functions on two-dimensional regions

Abstract

Weighted quasi-arithmetic means on two-dimensional regions are demonstrated, and risk averse conditions are discussed by the corresponding utility functions. For two utility functions on two-dimensional regions, we introduce a concept that decision making with one utility is more risk averse than decision making with the other utility. A necessary condition and a sufficient condition for the concept are demonstrated by their utility functions. Several examples are given to explain them.