Utility functions for wealth

We specify all utility functions on wealth implied by four special conditio ns on preferences between risky prospects in four theories of utility, unde r the presumption that preference increases in wealth. The theories are von Neumann-Morgenstern expected utility (EU), rank dependent utility (RDU), w eighted linear utility (WLU), and skew-symmetric bilinear utility (SSBU). T he special conditions are a weak version of risk neutrality, Pfanzagl's con sistency axiom, Bell's one-switch condition, and a contextual uncertainty c ondition. Previous research has identified the functional forms for utility of wealth for all four conditions under EU, and for risk neutrality and Pf anzagl's consistency axiom under WLU and SSBU. The functional forms for the other condition-theory combinations are derived in this paper.