Common Mathematical Foundations of Expected Utility and Dual Utility Theories

TL;DR

This paper unifies the core results of expected utility and dual utility theories using convex analysis and functional analysis, revealing their dual nature and deriving new integral representations.

Contribution

It introduces a unified mathematical framework for expected and dual utility theories, highlighting their duality and providing new integral representations.

Findings

Unified derivation of utility theories from convex and functional analysis

Revealed the dual character of utility functions

Derived new integral representations of dual utility models

Abstract

We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models.