ORIGINAL RESEARCH Alternative utility functions: review, analysis and comparison Arie Harel 1 • Jack Clark Francis 1,2 • Giora Harpaz 1 Ó Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The paper reviews the development of von Neumann and Morgenstern (vNM) utility theory. Kahneman and Tversky’s (KT’s) prospect theory is introduced. The vNM utility function is compared and contrasted with KT’s value function. We prove the uniqueness of two popular utility functions. First, we show that all power utility functions possess constant RRA. And, we show that all exponential utility functions have constant ARA. The paper concludes by discussing applications, strengths and weaknesses of various utility functions. Keywords von Neumann–Morgenstern (vNM) utility theory  Expected utility theory  Kahneman and Tversky (KT)  Prospect theory  Framing  Loss aversion  Risk aversion  Risk taking  Absolute risk aversion (ARA)  Relative risk aversion (RRA)  Subjective probabilities  Decision weights  Objective probabilities  Probability weighting JEL Classification G02  G10  D81 & Jack Clark Francis jack@jcfrancis.com Arie Harel Arie.Harel@Baruch.CUNY.edu Giora Harpaz Giora.Harpaz@Baruch.CUNY.edu 1 Zicklin School of Business, Bernard Baruch College, City University of New York (CUNY), One Bernard Baruch Way, New York, NY 10010-5585, USA 2 129 Old North Stamford Road, Stamford, CT 06905, USA 123 Rev Quant Finan Acc https://doi.org/10.1007/s11156-017-0688-z