Investment Under Demand Uncertainty: the Newsboy Problem Revisited.

In this article we study the effect of uncertainty on an entrepreneur who must choose the capacity of his business before knowing the demand for his product. The unit profit of operation is known with certainty but there is no flexibility in our one-period framework. We show how the introduction of global uncertainty reduces the investment of the risk neutral entrepreneur and, even more, that the risk averse one. We also show how marginal increases in risk reduce the optimal capacity of both the risk neutral and the risk averse entrepreneur, without any restriction on the concave utility function and with limited restrictions on the definition of a mean preserving spread. These general results are explained by the fact that the newsboy has a piecewise-linear, and concave, monetary payoff witha kink endogenously determined at the level of optimal capacity. Our results are compared with those in the two literatures on price uncertainty and demand uncertainty, and particularly, with the recent contributions of Eeckhoudt, Gollier and Schlesinger (1991, 1995).

Statistical Inference for Computable General Equilibrium Models with Application to a Model of the Moroccan Economy

We study the problem of measuring the uncertainty of CGE (or RBC)-type model simulations associated with parameter uncertainty. We describe two approaches for building confidence sets on model endogenous variables. The first one uses a standard Wald-type statistic. The second approach assumes that a confidence set (sampling or Bayesian) is available for the free parameters, from which confidence sets are derived by a projection technique. The latter has two advantages: first, confidence set validity is not affected by model nonlinearities; second, we can easily build simultaneous confidence intervals for an unlimited number of variables. We study conditions under which these confidence sets take the form of intervals and show they can be implemented using standard methods for solving CGE models. We present an application to a CGE model of the Moroccan economy to study the effects of policy-induced increases of transfers from Moroccan expatriates.

Relative Uncertainty and Additively Representable Set Rankings

This paper proposes a definition of relative uncertainty aversion for decision models under complete uncertainty. It is shown that, for a large class of decision rules characterized by a set of plausible axioms, the new criterion yields a complete ranking of those rules with respect to the relative degree of uncertainty aversion they represent. In addition, we address a combinatorial question that arises in this context, and we examine conditions for the additive representability of our rules.

Investment Under Demand Uncertainty: the Newsboy Problem Revisited.

In this article we study the effect of uncertainty on an entrepreneur who must choose the capacity of his business before knowing the demand for his product. The unit profit of operation is known with certainty but there is no flexibility in our one-period framework. We show how the introduction of global uncertainty reduces the investment of the risk neutral entrepreneur and, even more, that the risk averse one. We also show how marginal increases in risk reduce the optimal capacity of both the risk neutral and the risk averse entrepreneur, without any restriction on the concave utility function and with limited restrictions on the definition of a mean preserving spread. These general results are explained by the fact that the newsboy has a piecewise-linear, and concave, monetary payoff witha kink endogenously determined at the level of optimal capacity. Our results are compared with those in the two literatures on price uncertainty and demand uncertainty, and particularly, with the recent contributions of Eeckhoudt, Gollier and Schlesinger (1991, 1995).

The Efficient Use of Multiple Sources of a Nonrenewable Resource under Supply Cost Uncertainty

Uncertainties as to future supply costs of nonrenewable natural resources, such as oil and gas, raise the issue of the choice of supply sources. In a perfectly deterministic world, an efficient use of multiple sources of supply requires that any given market exhausts the supply it can draw from a low cost source before moving on to a higher cost one; supply sources should be exploited in strict sequence of increasing marginal cost, with a high cost source being left untouched as long as a less costly source is available. We find that this may not be the efficient thing to do in a stochastic world. We show that there exist conditions under which it can be efficient to use a risky supply source in order to conserve a cheaper non risky source. The benefit of doing this comes from the fact that it leaves open the possibility of using it instead of the risky source in the event the latter’s future cost conditions suddenly deteriorate. There are also conditions under which it will be efficient to use a more costly non risky source while a less costly risky source is still available. The reason is that this conserves the less costly risky source in order to use it in the event of a possible future drop in its cost.

Calibration de systèmes de caméras et projecteurs dans des applications de création multimédia

Ce mémoire s'intéresse à la vision par ordinateur appliquée à des projets d'art technologique. Le sujet traité est la calibration de systèmes de caméras et de projecteurs dans des applications de suivi et de reconstruction 3D en arts visuels et en art performatif. Le mémoire s'articule autour de deux collaborations avec les artistes québécois Daniel Danis et Nicolas Reeves. La géométrie projective et les méthodes de calibration classiques telles que la calibration planaire et la calibration par géométrie épipolaire sont présentées pour introduire les techniques utilisées dans ces deux projets. La collaboration avec Nicolas Reeves consiste à calibrer un système caméra-projecteur sur tête robotisée pour projeter des vidéos en temps réel sur des écrans cubiques mobiles. En plus d'appliquer des méthodes de calibration classiques, nous proposons une nouvelle technique de calibration de la pose d'une caméra sur tête robotisée. Cette technique utilise des plans elliptiques générés par l'observation d'un seul point dans le monde pour déterminer la pose de la caméra par rapport au centre de rotation de la tête robotisée. Le projet avec le metteur en scène Daniel Danis aborde les techniques de calibration de systèmes multi-caméras. Pour son projet de théâtre, nous avons développé un algorithme de calibration d'un réseau de caméras wiimotes. Cette technique basée sur la géométrie épipolaire permet de faire de la reconstruction 3D d'une trajectoire dans un grand volume à un coût minime. Les résultats des techniques de calibration développées sont présentés, de même que leur utilisation dans des contextes réels de performance devant public.

Étude des facteurs de perturbation de chambres d’ionisation sous conditions non standard

Durant la dernière décennie, les développements technologiques en radiothérapie ont transformé considérablement les techniques de traitement. Les nouveaux faisceaux non standard améliorent la conformité de la dose aux volumes cibles, mais également complexifient les procédures dosimétriques. Puisque des études récentes ont démontré l’invalidité de ces protocoles actuels avec les faisceaux non standard, un nouveau protocole applicable à la dosimétrie de référence de ces faisceaux est en préparation par l’IAEA-AAPM. Le but premier de cette étude est de caractériser les facteurs responsables des corrections non unitaires en dosimétrie des faisceaux non standard, et ainsi fournir des solutions conceptuelles afin de minimiser l’ordre de grandeur des corrections proposées dans le nouveau formalisme de l’IAEA-AAPM. Le deuxième but de l’étude est de construire des méthodes servant à estimer les incertitudes d’une manière exacte en dosimétrie non standard, et d’évaluer les niveaux d’incertitudes réalistes pouvant être obtenus dans des situations cliniques. Les résultats de l’étude démontrent que de rapporter la dose au volume sensible de la chambre remplie d’eau réduit la correction d’environ la moitié sous de hauts gradients de dose. Une relation théorique entre le facteur de correction de champs non standard idéaux et le facteur de gradient du champ de référence est obtenue. En dosimétrie par film radiochromique, des niveaux d’incertitude de l’ordre de 0.3% sont obtenus par l’application d’une procédure stricte, ce qui démontre un intérêt potentiel pour les mesures de faisceaux non standard. Les résultats suggèrent également que les incertitudes expérimentales des faisceaux non standard doivent être considérées sérieusement, que ce soit durant les procédures quotidiennes de vérification ou durant les procédures de calibration. De plus, ces incertitudes pourraient être un facteur limitatif dans la nouvelle génération de protocoles.

Revealed Preference and Choice under Uncertainty

We employ the theory of rational choice to examine whether observable choices from feasible sets of prospects can be generated by the optimization of some underlying decision criterion under uncertainty. Rather than focusing on a specific theory of choice, our objective is to formulate a general approach that is designed to cover the various decision criteria that have been proposed in the literature. We use a mild dominance property to define a class of suitable choice criteria. In addition to rationalizability per se, we characterize transitive and Suzumura consistent rationalizability in the presence of dominance.

Actuarial applications of multivariate phase-type distributions : model calibration and credibility

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Contracting for innovation under knightian uncertainty

At any given point in time, the collection of assets existing in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not publicly known along with an asset (in a broad sense) that pays contingent on those states. The creator of an innovation is an entrepreneur. He is represented by a probability measure on the set of new states. All other agents perceive the innovation as ambiguous: each of them is represented by a set of probabilities on the new states. The agents in the economy are classified with respect to their attitude towards this Ambiguity: the financiers are (locally) Ambiguity-seeking while the consumers are Ambiguity-averse. An entrepreneur and a financier come together when the former seeks funds to implement his project and the latter seeks new profit opportunities. The resulting contracting problem does not fall within the standard theory due to the presence of Ambiguity (on the financier’s side) and to the heterogeneity in the parties’ beliefs. We prove existence and monotonicity (i.e., truthful revelation) of an optimal contract. We characterize such a contract under the additional assumption that the financiers are globally Ambiguity-seeking. Finally, we re-formulate our results in an insurance framework and extend the classical result of Arrow [4] and the more recent one of Ghossoub. In the case of an Ambiguity-averse insurer, we also show that an optimal contract has the form of a generalized deductible.