On expected and von Neumann-Morgenstern utility functions

TL;DR

This paper explores the relationship between von Neumann-Morgenstern utility functions and expected utility functions, showing how properties like regularity and concavity transfer between them under certain assumptions.

Contribution

It establishes that regularity and concavity properties of expected utility functions can be inferred from those of von Neumann-Morgenstern utility functions.

Findings

Expected utility properties follow from von Neumann-Morgenstern utility functions under regularity and concavity.

The paper clarifies the transfer of classical utility function properties between the two frameworks.

Provides theoretical insights into the relationship between different utility function classes.

Abstract

In this note we analyze the relationship between the properties of von Neumann-Morgenstern utility functions and expected utility functions. More precisely, we investigate which of the regularity and concavity assumptions usually imposed on the latter transfer to the former and vice versa. In particular we obtain that, in order for the expected utility functions to fulfill such classical properties, it is enough to assume them for the von Neumann-Morgenstern utility functions.