Range and Sign Dependent Utility for Risk and Time

Abstract

We introduce range and sign dependent utility, an integrative behavioral model for uncertain cash flows. For gambles played today, the model can be seen as an extension of original prospect theory based on range, rather than rank. For single future payouts, the model agrees with hyperbolic discounting; whereas for multiple cash flows it takes a novel form. The model comes with a framing rule to set the range and the reference point, and three functions: a loss averse value function, a s-shaped range distortion function, and a subjective survival function for time. Range and sign dependent utility jointly explains the classical Allais paradoxes, the Samuelson paradox for risk and time, the preference reversal phenomenon and, for time, decreasing impatience and magnitude effects.