Weighted quasi-arithmetic mean on two-dimensional regions and their applications

Abstract

This paper discusses a decision maker’s attitude regarding risks, for example risk neutral, risk averse and risk loving in microeconomics by the convexity and concavity of utility functions. Weighted quasi-arithmetic means on two-dimensional regions are introduced, and some conditions on utility functions are discussed to characterize the decision maker’s attitude. Risk premiums on two-dimensional regions are given and demonstrated. Some approaches to construct two-dimensional utilities from one-dimensional ones are given, and a lot of examples of weighted quasi-arithmetic means are shown.