TITLE:
From Decision in Risk to Decision in Time (and Return)
AUTHORS:
Marc-Arthur Diaye, André Lapidus, Christian Schmidt
KEYWORDS:
Probability Discounting, Time Discounting, Logarithmic Time Perception, Rank-Dependent Utility, Rationality, Attitude Toward Probabilities, Attitude Toward Risk
JOURNAL NAME:
Theoretical Economics Letters,
Vol.14 No.5,
October
31,
2024
ABSTRACT: This paper aims to restate, in a decision theory framework, the results of some significant contributions of the literature on probability discounting that followed the publication of the pioneering article by Rachlin et al. We provide a restatement of probability discounting, usually limited to the case of 2-issues lotteries, in terms of rank-dependent utility, in which the utilities of the outcomes of n-issues lotteries are weighted by probabilities transformed after their transposition into time-delays. 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: a parameter related to impatience and pessimism, and a parameter related to time-consistency and the separation between non-optimism and non-pessimism. A simulation illustrates these results through the characteristics of the transformation of probabilities function.