An interesting literature in management science and operations research has dealt with the link between expected utility, risk and preference switches over gambles due to changes in wealth. However, no attention is paid to the specific nature of the gambles. All gambles are essentially assumed additive and, as such, do not address investment problems. By considering multiplicative gambles and more complicated risk exposures, the authors extend this literature to identify a rich set of commonly used utility functions, risk characteristics and risk measures consistent with investors who allow different numbers of switches between different types of gambles. This insight provides a new say of looking at popular utility functions, complementing risk aversion or stochastic dominance rules.
