The Use of Distribution Functions to Represent Utility Functions

This paper considers the decision maker whose evaluation and consequent choice of actions is accomplished through the use of the expected utility hypothesis. In cases where the utility function is increasing with upper and lower bounds then the utility function can be characterized by a distribution function, and we can take advantage of the various properties of such functions as well as existing results with respect to such functions. Using these properties and results we can determine the certainty equivalents as a function of the parameters of the distribution function (utility function) and the parameters of the probability distribution on the uncertain payoff. The following cases are considered: (1) Gaussian distribution function and Gaussian probability distribution, (2) Exponential distribution function and exponential distribution and (3) Exponential distribution function and Gaussian probability distribution.