Expected Utility Inequalities

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 infor-mation alone I develop upper bounds for the tails of the probabilis-tic belief about X of the decision maker. 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, credit risk and the equity premium puzzle. I would like to thank John Cochrane, Tom Cosimano, George Korniotis and Paul Schultz for helpful discussions and to participants at two Notre Dame seminars for their very useful comments. I began working on this project during a year-long visit to the Cen-tral Bank of Venezuela. I gratefully acknowledge their hospitality and \u85nancial support