In a stochastic environment, consumer preferences reflect their attitudes toward risk. These attitudes affect equilibrium asset prices and the nature of the equilibrium allocations. In this chapter, we describe expected utility preferences, which are additive across possible states of the world. We also define alternative measures of risk aversion and show their relationship to consumers' optimal portfolio choices.

Alternative utility functions imply different attitudes to risk by consumers. We examine the implications of risk aversion for a commonly used set of utility functions. We also discuss such concepts of increasing risk as stochastic dominance and a mean-preserving spread. These notions make precise the idea that a given situation under uncertainty is more risky relative to another, and allow us to examine the impact of increases in risk on consumer choices.

EXPECTED UTILITY PREFERENCES

The vast majority of consumer choice under uncertainty assumes expected utility maximization by consumers. In our previous analysis, we merely postulated the existence of expected utility preferences.

Some definitions

Expected utility preferences may be derived in an axiomatic way in a manner that is similar to the derivation of standard utility functions. According to the approach followed by von Neumann and Morgenstern [439], agents are assumed to have preferences over lotteries which are specified in terms of a set of payoffs and their probabilities.