Postprint version. Published in Economic Theory, Volume 36, Issue 1, July 1, 2008, pages 147-158.
The definitive version is available at https://doi.org/10.1007/s00199-007-0272-1.
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.