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1	Optimal sequential selection of a gambler assessed by the prophet Laumann, Werner 09 March 2001 (has links) In this thesis an optimal stopping problem related to the classical secretary problem is studied. The theory of optimal stopping represents a special branch of stochastic optimization. Here the socalled full information best choice problem with a known number of offers is generalized by maximizing the probability of selecting an r-candidate, where an offer is called r-candidate if it is not lower than the maximal offer reduced by function r. In the first part discrete time is investigated. For this optimal stopping problem to select an r-candidate an optimal stopping time is indicated, the suboptimal myopic stopping time is displayed and threshold rules are studied including asymptotic behaviour. The basis of this optimal stopping problem is displayed in a general setting where the payoff depends on the prophet´s choiceand on the maximal offer, i.e. the value of the prophet. As a further application the mean of the ratio of the gambler´s choice and prophet´s value is investigated. Then in the second part offers arrive in continuous time. Offers are presented according to random arrival times and the horizon terminating the period of choosing is taken to be fixed and random. Here stress is layed on the geometric and on the exponential distribution, i.e. the Poisson process. In the final part the optimal stopping problem of maximizing the duration of owning a sufficiently good offer is applied to the concept of an r-candidate. A distinction between an overall and a temporary r-candidate is made. The duration of owning an r-candidate is investigated for a finite number of offers with regard to recall. The duration problem with discounted epochs is resolved. Finally the duration of owning an r-candidate is considered regarding the Poisson process where the horizon is fixed and exponentially distributed. full information best choice secretary problem candidate problem duration problem 62L15 60G40 91A60 27 - Mathematik ddc:510
2	Sequential stopping under different environments of weak information Dendievel, Rémi 10 November 2016 (has links) (PDF) Notre thèse s’articule autour du thème de l’utilisation optimale de l’information contenue dans un modèle probabiliste flexible. Dans le premier chapitre, nous couvrons des résultats bien connus des martingales comme le théorème de convergence dit L1 des martingales et le théorème d’arrêt. Nous discutons de problèmes ouverts similaires au «last arrival problem» (Bruss et Yor, 2012) qui sont des vrais défis du point de vue théorique et nous ne pouvons que conjecturer la stratégie optimale.Dans les chapitres suivants, nous résolvons des extensions de problèmes d’arrêt optimal proposés par R. R. Weber (U. Cambridge), basés sur le «théorème des odds» (Bruss, 2000). En résumé, il s’agit d’effectuer une seule action (un seul arrêt) lorsque deux suites d’observations indépendantes sont observées simultanément. Nous donnons la solution à ces problèmes pour un nombre (fixé) choisi de processus.Le chapitre suivant passe en revue la plupart des développements récents (depuis 2000) réalisés autour du «théorème des odds» (Bruss, 2000). Le matériel présenté fut publié (2013), il a donc été mis à jour dans cette thèse pour inclure les derniers résultats depuis cette date.Puis nous réservons un chapitre pour une solution explicite pour un cas particulier du Problème d’arrêt optimal de Robbins. Ce chapitre est basé sur un article publié par l’auteur en collaboration avec le professeur Swan (Université de Liège). Ce chapitre offre une belle illustration des difficultés rencontrées lorsque trop d’information sur les variables est contenue dans le modèle. La solution optimale de ce problème dans le cas général n’est pas connue. Par contre, contre-intuitivement, dans le «last arrival problem» mentionné plus haut, moins d’information permet, comme nous le montrons, de trouver en effet la solution optimale.La thèse contient un dernier chapitre sur un problème de nature plus combinatoire que nous pouvons lier à la théorie des graphes dans une certaine mesure. Nous étudions le processus de création d’un graphe aléatoire particulier et les propriétés des cycles créés par celui-ci. Le problème est séquentiel et permet d’envisager des problèmes d’arrêt intéressants. Cette étude a des conséquences en théorie des graphes, en analyse combinatoire ainsi qu’en science de la chimie combinatoire pour les applications. Un de nos résultats est analogue au résultat de Janson (1987) relatif au premier cycle créé pendant la création de graphes aléatoires. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished Probabilités Processus stochastiques
3	Law in 3-Dimensions 2013 March 1900 (has links) This project, overall, involves a theory of law as dimensions. Throughout the history of the study of law, many different theoretical paradigms have emerged proffering different and competing ways to answer the question ‘what is law’? Traditionally, many of these paradigms have been at irreconcilable odds with one another. Notwithstanding this seeming reality, the goal of this project was to attempt to take three of the leading paradigms in legal theory and provide a way to explain how each might fit into a single coherent theory of law. I set out to accomplish this by drawing on the field of theoretical physics and that field’s use of spatial dimensions in explaining various physical phenomena. By engaging in a dimensional analysis of law, I found that I was able to place each paradigm within its own dimension with that dimension being defined by a specific element of time, and in doing so much of the conflict between the paradigms came to be ameliorated. The project has been divided into two main parts. PART I discusses the fundamentals of legal theory (Chapter 1) and the fundamentals of dimensions (Chapter 2). These fundamentals provide a foundation for a dimensional analysis of law which takes place throughout PART II. In Chapter 3, I argue that the three fundamental theses of Positivism coalesce with the 1st-dimension of law, which is defined as law as it exists at any one point in time. From there, I argue in Chapter 4 that the 2nd-dimension of law, being law as it exists between two points in time (i.e. when cases are adjudicated), is characterized by Pragmatism. I then turn, in Chapter 5, to argue that the 3rd-dimension of law, being law as it exists from the very first point in legal time to the ever changing present day, coalesces with the fundamental theses of Naturalism. Ultimately then, I argue that a theory of law as dimensions, through the vantage points of the specific elements of time, provides a more complete account of the nature of law. Legal Theory Jurisprudence Philosophy of Law Legal Positivism Positive Law Natural Law Pragmatism Inclusive Positivism Exclusive Positivism Interpretation Hart Dworkin Posner Finnis Fuller Gardner Shapiro Hume Elements of Time Dimensions Constitutional Law Morality Morals Separation Legal Reasoning Lawyers Law Necessary Connection Multiple Right Answer Best Choice Principle Practicality Judicial Adjudication Point in Time Audacity of Morality Law's True Ambition What is Law? Theoretical Physics Double Bind Multiple Bind First-Order Considerations Second-Order Considerations Penumbra Purity General Goal Incommensurable Legal System Wicked Legal System.

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