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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 information alone I develop upper bounds for the tails of the probabilistic 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.