Introduction

Stochastic dominance concerns the assessment and comparative statics of risk. It asks: What is meant by one prospect being more risky than another? A natural complementary issue concerns the problem of characterizing agents' attitude towards risk. We close this part with a brief discussion of this issue. In particular, we ask: What is meant by one agent being more risk-averse than another, how are these differences measured, and how useful are these measures in illuminating economic issues?

The Arrow–Pratt measures are the best-known measures of risk aversion. They are widely used to characterize the optimal allocation of risk, ranging from the demand for insurance and portfolio selection to the analysis of tax evasion. However, despite their success, these measures are not strong enough to always yield economically plausible results. This becomes apparent when they are applied to an incomplete-markets framework where agents cannot cover all risks.

The purpose of this brief chapter is to introduce important measures of risk aversion, spell out typical applications, and point out limitations and open issues. In particular, we address the following questions:

1. How should risk aversion be measured?

2. Is more risk aversion associated with a higher willingness to pay for insurance?

3. Should a more risk-averse investor hold more high-risk assets in his portfolio?

4. Should wealthier agents exhibit lower risk premiums or hold more high-risk assets if risk aversion is decreasing in wealth?