Compatibility of expected utility and <Emphasis Type="Italic">μ/σ</Emphasis> approaches to risk for a class of non location–scale distributions

Proofs of compatibility of the expected utility and μ/σ approaches to incorporating uncertainty in decision making exist for at least some utility functions and location–scale distributions. But there are severe constraints and it is desirable to investigate compatibility more widely. We do so for the class of distributions that are transformable to location–scale form by concave transformation and where the utility functions remain concave under transformation. The class is important, containing distributions such as the lognormal and Pareto, usually considered more appropriate for modelling income or wealth than those in the location–scale family. We are grateful to Jack Meyer for very helpful comments and discussions and also to an anonymous referee for useful remarks.