On the Necessary Condition for Linear Sharing and Separation: A Note - Huang, Chi-fu; Litzenberger, Robert (Journal of Financial and Quantitative Analysis, 1985)
A necessary and sufficient condition for linear sharing rules to be Pareto optimal, as generally accepted by the finance community, is that utility functions be of the equicautious HARA class. We demonstrate that this condition is not necessary for a fixed distribution of initial endowments and derive the necessary and sufficient condition. We show examples of utility functions satisfying our conditions.