The Pearson system of utility functions

This paper describes a parametric family of utility functions for decision analysis. The parameterization embeds the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions can have only four shapes: concave, convex, S-shaped, and reverse S-shaped. This makes the family suited for both expected utility and prospect theory. The paper also describes an alternative technique to estimate the four parameters from elicited utilities, which is simpler than standard fitting by minimization of the mean quadratic error.