Aspiration level, probability of success and failure, and expected utility

Aspiration levels are a relevant aspect of decision making. We develop a model that includes the overall probabilities of success and failure relative to the aspiration level into an expected utility representation. This turns out to be equivalent to expected utility with a discontinuous utility function. We give a behavioral foundation to the proposed model and provide conditions to determine the relative weights of the overall probabilities of success and failure. An aspiration level reinforces loss aversion, can account for simultaneous risk-averse and risk-seeking behavior, and can explain choices violating the mean-variance approach.