Expected utility inequalities: theory and applications

Suppose we know the utility function of a risk averse decision maker who values a risky prospect X at a price CE. Based on this information alone I develop upper bounds for the tails of the probabilistic belief about X of the decision maker. In the paper I also illustrate how to use these expected utility bounds in a variety of applications, which include the estimation of risk measures from observed data, option valuation, and the study of credit risk. I would like to thank John Cochrane, Tom Cosimano, Amanda Friedenberg, George Korniotis, Markus Brunermeier and Paul Schultz for helpful discussions and to participants at two Notre Dame seminars, at the 2006 Spring Midwest Economic Theory and International Economics Conference, and at the 2006 Australasian Meeting of the Econometric Society for their very useful comments. I began working on this project during a year-long visit to the Central Bank of Venezuela. I gratefully acknowledge their hospitality and financial support.