Delay Effect and Subadditivity. Proposal of a New Discount Function: The Asymmetric Exponential Discounting

Salvador Cruz Rambaud,Piedad Ortiz Fernández

doi:10.3390/math8030367

Abstract

The framework of this paper is intertemporal choice and, more specifically, the so-called delay effect. Traditionally, this anomaly, also known as decreasing impatience, has been revealed when individuals reverse their preferences over monetary or non-monetary rewards. In this manuscript, we will analyze the delay effect by using preference relations and discount functions. The treatment of the delay effect with discount functions exhibits several scenarios for this paradox. Thus, the objective of this paper is to deduce the different expressions of the delay effect and their mathematical characterizations by using discount functions in stationary and dynamic settings. In this context, subadditivity will be derived as a particular case of decreasing impatience. Finally, we will introduce a new discount function, the so-called asymmetric exponential discount function, able to describe decreasing impatience.

Highlights

The Discounted Utility model, originally introduced by Samuelson [1], became one of the main paradigms of asset valuation when time is involved in the decision-making
We are going to propose a novel dynamic discount function, the so-called asymmetric exponential discount function, which fits decreasing impatience better than the hyperbolic function of Mazur, since it exhibits the different types of delay effect presented in this work
This paper has dealt with the topic of the delay effect and decreasing impatience in intertemporal choice, one of the most important anomalies of the Discounted Utility model

Summary

Introduction

The Discounted Utility model, originally introduced by Samuelson [1], became one of the main paradigms of asset valuation when time is involved in the decision-making. This function exhibits a greater slope than the simple hyperbola presented by Mazur, reflecting the higher discount rates shown by decision-makers with problems of addiction. In this manuscript, we are going to propose a novel dynamic discount function, the so-called asymmetric exponential discount function, which fits decreasing impatience better than the hyperbolic function of Mazur, since it exhibits the different types of delay effect presented in this work.

Subadditivity

Dynamic

Proposal of a New Discounting Function

Result

Conclusions