From Decision in Risk to Decision in Time (and Return) a Restatement of Probability Discounting

Abstract

We provide a unifying framework in which according to the values of its parameters, we obtain the whole range of the properties of the probability weighting function usually acknowledged in the literature. This allows distinguishing between the different types (weak and strong) of pessimism and optimism toward probability, and to determine the various attitudes toward risk generated by the combination of a utility function and probability discounting. This formalism makes the typical cases of rationality in time and in risk mutually exclusive, but allows looser types of rationality. The resulting attitude toward probability and toward risk are then determined in relation to the values of the two parameters involved in the procedure of probability discounting.

Keywords: Probability discounting, time discounting, logarithmic time perception, rankdependent utility, rationality, attitude toward probabilities, attitude toward risk