On the Characterisation of Investor Preferences by Changes in Wealth

As wealth increases, preference of one fixed gamble over another typically changes once or not at all. A key question is whether certain assumptions on preferences guarantee such behaviour. Bell [Management Science, 34(12), 1416–1424, 1988; 41, 1145–1150, 1995a; 41(1), 23–30, 1995b] has addressed this difficult question and characterised the specific functional form of utility functions which allow a finite number of switches between two arbitrary gambles over the entire range of initial wealth. By extending this analysis, and linking the discussion to more recent works, the authors characterise conditions under which a large set of utility functions with respect to their switching characteristics, and discuss the results in the context of the classical notion of decreasing absolute risk aversion.