The gain-loss asymmetry and single-self preferences

Kahneman and Tversky asserted a fundamental asymmetry between gains and losses, namely a reflection effect which occurs when an individual prefers a sure gain of $ pz to anuncertain gain of $ z with probability p, while preferring an uncertain loss of $z with probability p to a certain loss of $ pz.We focus on this class of choices (actuarially fair), and explore the extent to which thereflection effect, understood as occurring at a range of wealth levels, is compatible with single-self preferences.We decompose the reflection effect into two components, a probability switch effect,which is compatible with single-self preferences, and a translation effect, which is not. To argue the first point, we analyze two classes of single-self, nonexpected utility preferences, which we label homothetic and weakly homothetic. In both cases, we characterize the switch effect as well as the dependence of risk attitudes on wealth.We also discuss two types of utility functions of a form reminiscent of expected utility but with distorted probabilities. Type I always distorts the probability of the worst outcome downwards, yielding attraction to small risks for all probabilities. Type II distorts low probabilities upwards, and high probabilities downwards, implying risk aversion when the probability of the worst outcome is low. By combining homothetic or weak homothetic preferences with Type I or Type II distortion functions, we present four explicit examples: All four display a switch effect and, hence, a form of reflection effect consistent a single self preferences.

Intergenerational justice when future worlds are uncertain

Let there be a positive (exogenous) probability that, at each date, the human species will disappear.We postulate an Ethical Observer (EO) who maximizes intertemporal welfare under thisuncertainty, with expected-utility preferences. Various social welfare criteria entail alternativevon Neumann- Morgenstern utility functions for the EO: utilitarian, Rawlsian, and an extensionof the latter that corrects for the size of population. Our analysis covers, first, a cake-eating economy(without production), where the utilitarian and Rawlsian recommend the same allocation.Second, a productive economy with education and capital, where it turns out that the recommendationsof the two EOs are in general different. But when the utilitarian program diverges, thenwe prove it is optimal for the extended Rawlsian to ignore the uncertainty concerning the possibledisappearance of the human species in the future. We conclude by discussing the implicationsfor intergenerational welfare maximization in the presence of global warming.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Consumption, investment and life insurance strategies with heterogeneous discounting

[cat] En aquest treball s'analitza l'efecte que comporta l'introducció de preferències inconsistents temporalment sobre les decisions òptimes de consum, inversió i compra d'assegurança de vida. En concret, es pretén recollir la creixent importància que un individu dóna a la herència que deixa i a la riquesa disponible per a la seva jubilació al llarg de la seva vida laboral. Amb aquesta finalitat, es parteix d'un model estocàstic en temps continu amb temps final aleatori, i s'introdueix el descompte heterogeni, considerant un agent amb una distribució de vida residual coneguda. Per tal d'obtenir solucions consistents temporalment es resol una equació de programació dinàmica no estàndard. Per al cas de funcions d'utilitat del tipus CRRA i CARA es troben solucions explícites. Finalment, els resultats obtinguts s'il·lustren numèricament.

Consumption, investment and life insurance strategies with heterogeneous discounting

[cat] En aquest treball s'analitza l'efecte que comporta l'introducció de preferències inconsistents temporalment sobre les decisions òptimes de consum, inversió i compra d'assegurança de vida. En concret, es pretén recollir la creixent importància que un individu dóna a la herència que deixa i a la riquesa disponible per a la seva jubilació al llarg de la seva vida laboral. Amb aquesta finalitat, es parteix d'un model estocàstic en temps continu amb temps final aleatori, i s'introdueix el descompte heterogeni, considerant un agent amb una distribució de vida residual coneguda. Per tal d'obtenir solucions consistents temporalment es resol una equació de programació dinàmica no estàndard. Per al cas de funcions d'utilitat del tipus CRRA i CARA es troben solucions explícites. Finalment, els resultats obtinguts s'il·lustren numèricament.

Bayesian Analysis for a Theory of Random Consumer Demand: The Case of Indivisible Goods

McCausland (2004a) describes a new theory of random consumer demand. Theoretically consistent random demand can be represented by a \"regular\" \"L-utility\" function on the consumption set X. The present paper is about Bayesian inference for regular L-utility functions. We express prior and posterior uncertainty in terms of distributions over the indefinite-dimensional parameter set of a flexible functional form. We propose a class of proper priors on the parameter set. The priors are flexible, in the sense that they put positive probability in the neighborhood of any L-utility function that is regular on a large subset bar(X) of X; and regular, in the sense that they assign zero probability to the set of L-utility functions that are irregular on bar(X). We propose methods of Bayesian inference for an environment with indivisible goods, leaving the more difficult case of indefinitely divisible goods for another paper. We analyse individual choice data from a consumer experiment described in Harbaugh et al. (2001).

Essais sur la conception de mécanismes et les enchères

Cette thèse est composée de trois essais liés à la conception de mécanisme et aux enchères. Dans le premier essai j'étudie la conception de mécanismes bayésiens efficaces dans des environnements où les fonctions d'utilité des agents dépendent de l'alternative choisie même lorsque ceux-ci ne participent pas au mécanisme. En plus d'une règle d'attribution et d'une règle de paiement le planificateur peut proférer des menaces afin d'inciter les agents à participer au mécanisme et de maximiser son propre surplus; Le planificateur peut présumer du type d'un agent qui ne participe pas. Je prouve que la solution du problème de conception peut être trouvée par un choix max-min des types présumés et des menaces. J'applique ceci à la conception d'une enchère multiple efficace lorsque la possession du bien par un acheteur a des externalités négatives sur les autres acheteurs. Le deuxième essai considère la règle du juste retour employée par l'agence spatiale européenne (ESA). Elle assure à chaque état membre un retour proportionnel à sa contribution, sous forme de contrats attribués à des sociétés venant de cet état. La règle du juste retour est en conflit avec le principe de la libre concurrence puisque des contrats ne sont pas nécessairement attribués aux sociétés qui font les offres les plus basses. Ceci a soulevé des discussions sur l'utilisation de cette règle: les grands états ayant des programmes spatiaux nationaux forts, voient sa stricte utilisation comme un obstacle à la compétitivité et à la rentabilité. Apriori cette règle semble plus coûteuse à l'agence que les enchères traditionnelles. Nous prouvons au contraire qu'une implémentation appropriée de la règle du juste retour peut la rendre moins coûteuse que des enchères traditionnelles de libre concurrence. Nous considérons le cas de l'information complète où les niveaux de technologie des firmes sont de notoriété publique, et le cas de l'information incomplète où les sociétés observent en privée leurs coûts de production. Enfin, dans le troisième essai je dérive un mécanisme optimal d'appel d'offre dans un environnement où un acheteur d'articles hétérogènes fait face a de potentiels fournisseurs de différents groupes, et est contraint de choisir une liste de gagnants qui est compatible avec des quotas assignés aux différents groupes. La règle optimale d'attribution consiste à assigner des niveaux de priorité aux fournisseurs sur la base des coûts individuels qu'ils rapportent au décideur. La manière dont ces niveaux de priorité sont déterminés est subjective mais connue de tous avant le déroulement de l'appel d'offre. Les différents coûts rapportés induisent des scores pour chaque liste potentielle de gagnant. Les articles sont alors achetés à la liste ayant les meilleurs scores, s'il n'est pas plus grand que la valeur de l'acheteur. Je montre également qu'en général il n'est pas optimal d'acheter les articles par des enchères séparées.

Should a non-rival public good always be provided centrally?

This paper discusses the problem of optimal design of a jurisdiction structure from the view point of a utilitarian social planner when individuals with identical utility functions for a non-rival public good and private consumption have private information about their contributive capacities. It shows that the superiority of a centralized provision of a non-rival public good over a federal one does not always hold. Specifically, when differences in individuals’ contributive capacities are large, it is better to provide the public good in several distinct jurisdictions rather than to pool these jurisdictions into a single one. In the specific situation where individuals have logarithmic utilities, the paper provides a complete characterization of the optimal jurisdiction structure in the two-type case.

The Human in the Loop: User Participation in Self-Adaptive Software

Self-adaptive software provides a profound solution for adapting applications to changing contexts in dynamic and heterogeneous environments. Having emerged from Autonomic Computing, it incorporates fully autonomous decision making based on predefined structural and behavioural models. The most common approach for architectural runtime adaptation is the MAPE-K adaptation loop implementing an external adaptation manager without manual user control. However, it has turned out that adaptation behaviour lacks acceptance if it does not correspond to a user’s expectations – particularly for Ubiquitous Computing scenarios with user interaction. Adaptations can be irritating and distracting if they are not appropriate for a certain situation. In general, uncertainty during development and at run-time causes problems with users being outside the adaptation loop. In a literature study, we analyse publications about self-adaptive software research. The results show a discrepancy between the motivated application domains, the maturity of examples, and the quality of evaluations on the one hand and the provided solutions on the other hand. Only few publications analysed the impact of their work on the user, but many employ user-oriented examples for motivation and demonstration. To incorporate the user within the adaptation loop and to deal with uncertainty, our proposed solutions enable user participation for interactive selfadaptive software while at the same time maintaining the benefits of intelligent autonomous behaviour. We define three dimensions of user participation, namely temporal, behavioural, and structural user participation. This dissertation contributes solutions for user participation in the temporal and behavioural dimension. The temporal dimension addresses the moment of adaptation which is classically determined by the self-adaptive system. We provide mechanisms allowing users to influence or to define the moment of adaptation. With our solution, users can have full control over the moment of adaptation or the self-adaptive software considers the user’s situation more appropriately. The behavioural dimension addresses the actual adaptation logic and the resulting run-time behaviour. Application behaviour is established during development and does not necessarily match the run-time expectations. Our contributions are three distinct solutions which allow users to make changes to the application’s runtime behaviour: dynamic utility functions, fuzzy-based reasoning, and learning-based reasoning. The foundation of our work is a notification and feedback solution that improves intelligibility and controllability of self-adaptive applications by implementing a bi-directional communication between self-adaptive software and the user. The different mechanisms from the temporal and behavioural participation dimension require the notification and feedback solution to inform users on adaptation actions and to provide a mechanism to influence adaptations. Case studies show the feasibility of the developed solutions. Moreover, an extensive user study with 62 participants was conducted to evaluate the impact of notifications before and after adaptations. Although the study revealed that there is no preference for a particular notification design, participants clearly appreciated intelligibility and controllability over autonomous adaptations.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution.

Aldose reductase and the importance of experimental design

Kinetic studies on the AR (aldose reductase) protein have shown that it does not behave as a classical enzyme in relation to ring aldose sugars. As with non-enzymatic glycation reactions, there is probably a free radical element involved derived from monosaccharide autoxidation. in the case of AR, there is free radical oxidation of NADPH by autoxidizing monosaccharides, which is enhanced in the presence of the NADPH-binding protein. Thus any assay for AR based on the oxidation of NADPH in the presence of autoxidizing monosaccharides is invalid, and tissue AR measurements based on this method are also invalid, and should be reassessed. AR exhibits broad specificity for both hydrophilic and hydrophobic aldehydes that suggests that the protein may be involved in detoxification. The last thing we would want to do is to inhibit it. ARIs (AR inhibitors) have a number of actions in the cell which are not specific, and which do not involve them binding to AR. These include peroxy-radical scavenging and effects of metal ion chelation. The AR/ARI story emphasizes the importance of correct experimental design in all biocatalytic experiments. Developing the use of Bayesian utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has led to the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-m and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimizes the error in the parameters estimated, and is suitable for simple or complex steady-state models.

A novel Bayesian approach to drug design with simple and complex enzymes: Use with lens aldehyde dehydrogenase and the glyoxalase pathway

Purpose: Acquiring details of kinetic parameters of enzymes is crucial to biochemical understanding, drug development, and clinical diagnosis in ocular diseases. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. Methods: We have developed Bayesian utility functions to minimise kinetic parameter variance involving differentiation of model expressions and matrix inversion. These have been applied to the simple kinetics of the enzymes in the glyoxalase pathway (of importance in posttranslational modification of proteins in cataract), and the complex kinetics of lens aldehyde dehydrogenase (also of relevance to cataract). Results: Our successful application of Bayesian statistics has allowed us to identify a set of rules for designing optimum kinetic experiments iteratively. Most importantly, the distribution of points in the range is critical; it is not simply a matter of even or multiple increases. At least 60 % must be below the KM (or plural if more than one dissociation constant) and 40% above. This choice halves the variance found using a simple even spread across the range.With both the glyoxalase system and lens aldehyde dehydrogenase we have significantly improved the variance of kinetic parameter estimation while reducing the number and costs of experiments. Conclusions: We have developed an optimal and iterative method for selecting features of design such as substrate range, number of measurements and choice of intermediate points. Our novel approach minimises parameter error and costs, and maximises experimental efficiency. It is applicable to many areas of ocular drug design, including receptor-ligand binding and immunoglobulin binding, and should be an important tool in ocular drug discovery.