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TWO‐PIECE VON NEUMANN‐MORGENSTERN UTILITY FUNCTIONS *
Author(s) -
Fishburn Peter C.,
Kochenberger Gary A.
Publication year - 1979
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1979.tb00043.x
Subject(s) - concave function , exponential function , regular polygon , exponential utility , mathematics , expected utility hypothesis , mathematical optimization , prospect theory , power function , econometrics , mathematical economics , economics , mathematical analysis , finance , geometry
Thirty empirically assessed utility functions on changes in wealth or return on investment were examined for general features and susceptability to fits by linear, power, and exponential functions. Separate fits were made to below‐target data and above‐target data. The usual “target” was the no‐change point. The majority of below‐target functions were risk seeking; the majority of above‐target functions were risk averse; and the most common composite shape was convex‐concave, or risk seeking in losses and risk averse in gains. The least common composite was concave‐concave. Below‐target utility was generally steeper than above‐target utility with a median below‐to‐above slope ratio of about 4.8. The power and exponential fits were substantially better than the linear fits. Power functions gave the best fits in the majority of convex below‐target and concave above‐target cases, and exponential functions gave the best fits in the majority of concave below‐target and convex above‐target cases. Several implications of these results for decision making under risk are mentioned.