Journal of Risk and Uncertainty

, Volume 20, Issue 1, pp 5–44 | Cite as

Utility Functions for Wealth

  • David E. Bell
  • Peter C. Fishburn


We specify all utility functions on wealth implied by four special conditions on preferences between risky prospects in four theories of utility, under the presumption that preference increases in wealth. The theories are von Neumann-Morgenstern expected utility (EU), rank dependent utility (RDU), weighted linear utility (WLU), and skew-symmetric bilinear utility (SSBU). The special conditions are a weak version of risk neutrality, Pfanzagl's consistency axiom, Bell's one-switch condition, and a contextual uncertainty condition. Previous research has identified the functional forms for utility of wealth for all four conditions under EU, and for risk neutrality and Pfanzagl's consistency axiom under WLU and SSBU. The functional forms for the other condition-theory combinations are derived in this paper.

expected utility rank dependent utility weighted utility skew-symmetric bilinear utility consistency axiom one-switch condition contextual uncertainty 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • David E. Bell
    • 1
  • Peter C. Fishburn
    • 2
  1. 1.Harvard Business SchoolBoston
  2. 2.AT&T Labs-Research

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