Intertemporal choices play a fundamental role in the lives of individuals, and the Discounted Utility model is the essential framework for describing decision makers’ attitudes in front of alternatives structured over multiple periods. The classical formulation of the model assumes constant preferences over time, i.e., it assumes that individuals’ choices are consistent. Empirical evidence, however, shows that individuals’ preferences do not respond to this assumption, generating temporally inconsistent decisions. This paper addresses the problem of temporal inconsistency in order to interpret and describe anomalous choices, i.e., not rationalizable from a theoretical point of view, through the cognitive distortions of the decision-maker. Indeed, even if we assume that the investor is a rational subject, behavioral finance suggests that an anomaly is part of the human being and must be recognized as a systematic condition of the decision-making process. Exploiting the relationship between the rate of impatience and temporal preference, this work aims to demonstrate that the degree of decrease in impatience quantifies the weight of emotional drives in the anomalies of intertemporal choices. An experimental approach based on constructing the hyperbolic factor for each individual in different contexts is presented to test our results. The variability in the collected data highlights that individuals’ behavior is very different, suggesting the need to project strategies in personalized finance.

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Intertemporal choices are those decisions structured over several periods in which the effects only manifest themselves with the passage of time. The main mathematical reference for studying the behavior of individuals with respect to this type of decision is the Discounted Utility Model which hypothesizes completely rational individuals. The empirical evidence that deviates from normative expectations has motivated the formulation of alternative models with the aim of better describing the behavior of individuals. The present paper investigates the characteristics behind hyperbolic discounting starting from the phenomenon of decision inconsistency, i.e., when individuals’ preferences vary over time. The mechanisms of inconsistency will be explored through the physical concept of relative time, proving the importance of uncertainty aversion in the hyperbolic trend of the discount function. The analysis of the mathematical characteristics of hyperbolic discounting and the relationship between decision inconsistency and subjective perception of time defines the maximum distance between rational and non-rational preferences. An experimental part empirically proves the relationship between uncertainty aversion and time inconsistency. The present paper contributes to the literature by defining a new characteristic of hyperbolic discounting and quantifying the impact of the subjective perception of time in the decision-making process.

The interval effect refers to the phenomenon in which the discount rate decreases as the interval considered increases. It represents one of the many anomalies of the decision-making process in the context of intertemporal choices. This paper suggests that the latter anomaly is due to the perceived time and emotional drives involved in the moment of choice and their interaction. The study is developed through a direct comparison between empirical preferences and those predicted by the normative model, respectively determined by proper time, i.e., empirical time and normative time, which are different from objective time. Although it was known in the literature that the perception of time has a substantial impact on preferences and the phenomenon of temporal inconsistency, our study presents a measure that quantifies the decision-making bias caused by the subjective perception of time and contributes to the normalisation of choices defined as irrational. By the term normalisation, we mean to clarify the extent to which the cognitive structures of the decision-maker respect the principles of economic rationality. From an operational point of view, the present work's originality lies in proving that the same description of subjective time is not constant in the context of the interval effect. The experimental implementation provides empirical evidence of the latter considerations. The contribution of this work refers mainly to the field of behavioural finance as it aims to describe anomalies as inevitable consequences of individual cognitive processes.

The aim of this paper is to present a methodology to generate a partially subadditive (respectively superadditive) discount function starting from an entirely subadditive (respectively superadditive) discount model. To do this, we are going to use the concept of deformation of time in a discount function, focusing on Stevens' power law. A deformation of time is a function that mathematically represents the perception from an individual or a group of individuals about how the calendar time evolves. This approach will be important when describing the treatment of addictions and other diseases in patients who show a certain degree of impulsivity in their intertemporal choice.