Essays on behavioral decision making

Este trabajo de tesis consiste en cuatro ensayos sobre la teoría de la toma de decisiones. El primer ensayo analiza las preferencias por las ganancias derivadas de la diversificación que tienen los agentes económicos de acuerdo la teoría del arrepentimiento. El segundo ensayo presenta nuevas desigualdades de la covarianza de funciones no monótonas de una variable aleatoria. Se muestran dos aplicaciones de estos nuevos resultados. El tercer ensayo propone una extensión de la heuristica del reconocimiento. En esta nueva propuesta se distinguen tres niveles de reconocimiento. Se compara el poder predictivo de esta heurística para vectores con tres y diez objetos. Por último, el cuarto ensayo analiza los principios de la contabilidad mental cuando los tomadores de decisiones deben integrar o segregar tres o más experiencias, resultados, etc

Prospect theory and hedging risks

The prospect theory is one of the most popular decision-making theories. It is based on the S-shaped utility function, unlike the von Neumann and Morgenstern (NM) theory, which is based on the concave utility function. The S-shape brings in mathematical challenges: simple extensions and generalizations of NM theory into the prospect theory cannot be frequently achieved. For example, the nature of monotonicity of the indifference curve depends on the underlying mean. Price hedging decisions also become more complex within the prospect theory. We discuss these topics in detail and offer a general result concerning the sign of a covariance from which we then infer desired properties of the indifference curve and also justify hedging decisions within the prospect theory. We illustrate our general considerations with a thoroughly worked out example. --prospect theory,mean-variance model,indifference curve,price uncertainty,hedging

Integration-segregation decisions under general value functions : "Create your own bundle -- choose 1, 2, or all 3 !"

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2012.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2012.57 - ISSN : 1955-611XWhether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance, and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call 'exposure units' to naturally cover manifold scenarios spanning well beyond 'products'. Our findings show, for example, that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e., all are gains) or all negative (i.e., all are losses). In the case of exposure units mixed-sign values, decision rules are much more complex and rely on cataloging the Bell-number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.Le choix de vendre des biens l'unité ou en "package" est un sujet d'intérêt dans de multiples applications telles que la théorie de portefeuille en finance, l'allocation du capital risque en assurance et le marketing de biens de consommation. De telles décisions sont complexes et dépendent de facteurs tels que la valeur sous-jacente des biens et les préférences des consommateurs. Dans cet article nous proposons des règles de décision pour des biens multiples et nous proposons une extension du fameux principe de Thaler de comptabilité mentale qui ne s'appliquait originellement qu'au cas de deux biens de même signe (gains ou pertes). Dans le cas de biens mixtes multiples, les décisions deviennent plus complexes et reposent sur les partitions des nombres de Bell qui augmentent de manière exponentielle avec le nombre de biens. Ainsi dans cet article, nous présentons des règles détaillées dans le choix d'intégrer ou de séparer trois biens ainsi que des règles partielles pour un nombre arbitraire de biens

General approach to coordinate representation of compositional tables

This is the peer reviewed version which has been published in final form at [https://doi.org/10.1111/sjos.12326]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.Compositional tables can be considered a continuous counterpart to the well-known contingency tables. Their cells, which generally contain positive real numbers rather than just counts, carry relative information about relationships between two factors. Hence, compositional tables can be seen as a generalization of (vector) compositional data. Due to their relative character, compositions are commonly expressed in orthonormal coordinates using a sequential binary partition prior to being further processed by standard statistical tools. Unfortunately, the resulting coordinates do not respect the two-dimensional nature of compositional tables. Information about relationship between factors is thus not well captured. The aim of this paper is to present a general system of orthonormal coordinates with respect to the Aitchison geometry, which allows for an analysis of the interactions between factors in a compositional table. This is achieved using logarithms of odds ratios, which are also widely used in the context of contingency tables

A composite Bayesian hierarchical model of compositional data with zeros

We present an effective approach for modelling compositional data with large concentrations of zeros and several levels of variation, applied to a database of elemental compositions of forensic glass of various use types. The procedure consists of the following: (i) partitioning the data set in subsets characterised by the same pattern of presence/absence of chemical elements and (ii) fitting a Bayesian hierarchical model to the transformed compositions in each data subset. We derive expressions for the posterior predictive probability that newly observed fragments of glass are of a certain use type and for computing the evidential value of glass fragments relating to two competing propositions about their source. The model is assessed using cross-validation, and it performs well in both the classification and evidence evaluation tasks

Some covariance inequalities for non-monotonic functions with applications to mean-variance indifference curves and bank hedging

In several problems of decision-making under uncertainty, it is necessary to study the sign of the covariance between marginal utilities. All of the works that study the covariance signs are based on Chebyschev’s integral inequality. However, this inequality requires that both functions be monotonic. There are many cases, originated basically by new alternative theories, which assume that the marginal utilities of interest are non-monotonic. Thus, we cannot use Chebyschev’s result as it relies on monotonic functions. In this article, I derive some new covariance inequalities for utility functions which have non-monotonic marginal utilities. I also apply the theoretical results to two problems in economics: First, I study some properties of the indiference curve in the mean-variance space for Prospect Theory and for Markowitz utility functions. Second, I analyze the asset hedging policies of a bank that behaves as predicted by Prospect Theory

A simple model for mixing intuition and analysis

Firefighters, emergency paramedics, and airplane pilots are able to make correct judgments and choices in challenging situations of scarce information and time pressure. Experts often attribute such successes to intuition and report that they avoid analysis. Similarly, laypeople can effortlessly perform tasks that confuse machine algorithms. OR should ideally respect human intuition while supporting and improving it with analytical modelling. We utilize research on intuitive decision making from psychology to build a model of mixing intuition and analysis over a set of interrelated tasks, where the choice of intuition or analysis in one task affects the choice in other tasks. In this model, people may use any analytical method, such as multi-attribute utility, or a single-cue heuristic, such as availability or recognition. The article makes two contributions. First, we study the model and derive a necessary and sufficient condition for the optimality of using a positive proportion of intuition (i.e., for some tasks): Intuition is more frequently accurate than analysis to a larger extent than analysis is more frequently accurate than guessing. Second, we apply the model to synthetic data and also natural data from a forecasting competition for a Wimbledon tennis tournament and a King's Fund study on how patients choose a London hospital: The optimal proportion of intuition is estimated to range from 25% to 53%. The accuracy benefit of using the optimal mix over analysis alone is estimated between 3% and 27%. Such improvements would be impactful over large numbers of choices as in public health.</p