Introduction

Expected utility provides a framework for the analysis of agents' attitudes toward risk. In this chapter we present a formal definition of risk aversion and introduce measures of the intensity of risk aversion such as the Arrow–Pratt measures and risk compensation. The main result of this chapter, the Pratt Theorem, establishes the equivalence of these different measures of risk aversion.

Agents' preferences over risky consumption plans are assumed to have an expected utility representation with continuous von Neumann–Morgenstern utility functions. The consumption plans in the domain of an expected utility function may be defined either narrowly or broadly. The axioms of expected utility imply that any consumption plan can be viewed as a random variable on the set S of states equipped with an agent's subjective probability measure. Thus, if the objects of choice are specified as the consumption plans that emerge from the axioms of expected utility, these are appropriately defined narrowly as random variables that can take S values with given probabilities. However, the analysis of this chapter applies equally well if consumption plans are broadly interpreted as arbitrary random variables (that is, as random variables with an arbitrary number of realizations and arbitrary probabilities). The choice between these interpretations is a matter of taste.

Except in Section 9.10, it is assumed that date-0 consumption does not enter the utility functions, and throughout it is assumed that there are at least two states at date 1, S ≥ 2.