Quantification of Aversion to Uncertainty in Intertemporal Choice through Subjective Perception of Time

Abstract

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.

An Analytic Network Process to Support Financial Decision-Making in the Context of Behavioural Finance

“…In this respect, intertemporal choice theory provides measures of behavioural and cognitive attitudes. In fact, recent studies [28,47] on the evolution of the discount function show how to quantify the relationship between uncertainty and decision-making under conditions of uncertainty. The measures used in this paper relate to two fundamental elements of the decision-making process: cognitive biases and subjective perception of time.…”

“…To calculate uncertainty aversion, one must first obtain the distance between the empirical and exponential trends of the individual discount functions. Of this distance over time, the maximum of the absolute values is considered, which indicates the maximum distance between the empirical preferences and those predicted by the DUM [28].…”

“…To improve profiling, behavioural finance research, which highlights the importance of cognitive and behavioural attitudes in obtaining a rich description of the decisionmaker, should be added to the previous five classes [27]. In addition, recent research has demonstrated a quantifiable cognitive dimension when evaluating temporal alternatives under uncertainty [18,28,29]. Thus, other clusters can be included and implemented to include behavioural finance studies and the dimension of uncertainty in decision-making.…”

“…The degree to which impatience decreases over time is behaviourally related to emotional drives that intervene during decision-making and result in anomalous preferences [18]. The second measure, on the other hand, is a measure of the decision-maker's non-rationality obtained as the distance between empirical and exponential preferences [28,34]. This measure is expressed in relation to the subjective perception of time and quantifies the degree of uncertainty aversion.…”

“…Risk tolerance is related to uncertainty aversion and the degree of decreasing impatience to express how uncertainty management could affect risk tolerance, and vice versa; • Uncertainty aversion and the degree of decreasing impatience are related because they are both different characteristics of a discount with a non-exponential trend [28].…”