Cette thèse se compose de cinq parties indépendantes dédiées à la modélisation et à l’étude des problèmes liés au risque du défaut, en information partielle. La première partie constitue l’Introduction. La deuxième partie est dédiée au calcul de la probabilité de survie d’une firme, conditionnellement à l’information à disposition de l’investisseur, dans un modèle structurel en information partielle. On utilise une technique numérique hybride basée sur la méthode Monte Carlo et la quantification optimale. Dans la troisième partie on traite, avec l’approche Programmation Dynamique, un problème en temps discret de maximisation de l’utilité de la richesse terminale, dans un marché où des titres soumis au risque du défaut sont négociés. Le risque de contagion entre les défauts est modélisé, ainsi que la possible incertitude du modèle. Dans la quatrième partie on s’intéresse au problème de l’incertitude liée à l’horizon temporel d’investissement. Dans un marché complet soumis au risque du défaut, on résout, soit avec la méthode martingale, soit avec la Programmation Dynamique, trois problèmes de maximisation de l’utilité de la consommation: quand l’horizon temporel est fixe, fini mais incertain et infini. Enfin, dans la cinquième partie on traite un problème purement théorique. Dans le contexte du grossissement de filtrations, notre but est de redémontrer, dans un cadre spécifique, les résultats déjà connus sur la caractérisation des martingales, la décomposition des martingales par rapport à la filtration de référence comme semimartingales dans les filtrations progressivement et initialement grossies et le Théorème de Représentation Prévisible. / This Ph.D. thesis consists of five independent parts devoted to the modeling and to studying problems related to default risk, under partial information. The first part constitutes the Introduction. The second part is devoted to the computation of survival probabilities of a firm, conditionally to the information available to the investor, in a structural model, under partial information. We exploit a numerical hybrid technique based on the application of the Monte Carlo method and of optimal quantization. In the third part we deal, by means of the Dynamic Programming, with a discrete time maximization of the expected utility from terminal wealth problem, in a market where defaultable assets are traded. Contagion risk between the default times is modeled, as well as model uncertainty, by working under partial information. In the fourth part we are interested in studying the problem linked to the uncertainty of the investment horizon. In a complete market model subject to default risk, we solve, both with the martingale method and with the Dynamic Programming, three different problems of maximization of expected utility from consumption: when the investment horizon is fixed, finite but uncertain, and infinite. Finally, in the fifth part we deal with a purely theoretical problem. In the context of enlargement of filtrations our aim is to retrieve, in a specific setting, the already known results on martingales’ characterization, on the decomposition of martingales with respect to the reference filtration as semi-martingales in the progressively and in the initially enlarged filtrations and the Predictable Representation Theorem.

This research proposes a methodology to solve distributed optimization problems where quasi-autonomous decision entities directly interact with each other for partial information sharing. In the distributed system we study the quasi-autonomy arising from the assumption that each decision entity has complete and unique responsibility for a subset of decision variables. However, when solving a decision problem locally, consideration is given to how the local decisions affect overall system performance such that close-to-optimal solutions are obtained among all participating decision entities. Partial information sharing refers to the fact that no entity has the complete information access needed to solve the optimization problem globally. This condition hinders the direct application of traditional optimization solution methods. In this research, it is further assumed that direct interaction among the decision entities is allowed. This compensates for the lack of complete information access with the interactive exchange of non-private information. The methodology is tested in different application contexts: manufacturing capacity allocation, single machine scheduling, and jobshop scheduling. The experimental results show that the proposed method generates close-to optimal solutions in the tested problem settings.

Στη παρούσα διπλωματική εργασία παρουσιάζεται η ανάπτυξη κώδικα σε γλώσσα προγραμματισμού Python με σκοπό να παίζει το παιχνίδι Bluff. Αναλυτικότερα το Bluff ανήκει στη κατηγορία των παιχνιδιών μερικούς πληροφόρησης και εκδοχές του περιλαμβάνουν το στοιχείο της τύχης άρα είναι και στοχαστικό. Στην ίδια κατηγορία παιχνιδιών εντάσεται και το πόκερ στο οποίο διεξάγεται εντονη ερευνητική δραστηριότητα αυτή τη περίοδο. Οι δυσκολίες που παρουσιάζει το εγχείρημα της κατασκευης ενός τέτοιου αλγόριθμου εγκειται στο μεγάλο χώρο καταστασης του παιχνιδιού και στην αδυναμια εφαρμογης της τεχνικής min max λόγω της δομής του παιχνιδιού. Επίσης ενας επιτυχημένος παίχτης bluff θα πρέπει να αναγνωρίζει ποτε ο αντίπαλος μπλοφάρει καθώς και να μπλοφάρει ο ίδιος. Τέλος όπως και στο ποκερ για να γίνεις μετρ στο παιχνίδι θα πρέπει να μεταβάλεις τη στρατηγική σου ανάλογα με τον αντίπαλο, θα πρέπει να εκμεταλεύεσαι τα λάθη του και ταυτόχρονα να μη γίνεσαι προβλέψιμος. Ο κώδικας μας εχει 3 versions. Στη πρώτη version ενας απλος μηχανισμός που στηρίζεται στους κανονες του παιχνιδίου υλοποιείται και εξετάζεται η επιτυχια του. Στη δευτερη εκδοση εισαγουμε το στοιχειο της μπλόφας ενώ στη τρίτη αφου μοντελοποιήσουμε τον αντίπαλο, λαμβάνουμε αποφάσεις με βάση αυτη τη μοντελοποίηση. / This diploma thesis deals with the problem of developing an algorithm that can play the game of Bluff. The programming language that is used is Python. Concretely the game of bluff belongs into the category of partial information games and some variations involve luck which makes it also stochastic. Intense research is conducted in poker which belongs to the same family of games. The main difficulty is the huge state space of these games due to uncertainty and the deficit of the min-max method. In addition a succesfull bluff player must recognize when the opponent is bluffing and must make bluffs on his own. One last thing that this game requires is to have dynamic strategies which means being able to change your strategy according to the opponent in order to maximize your wining by exploiting his errors. The algorithm builded has 3 versions. The first one simulated a beginner that sticks to the rules, makes no bluffs and raises according to probabilities. The second version introduces bluffing. The final version includes opponent modeling and making decision based on that.

In der Arbeit befassen wir uns mit der Potenznutzenmaximierung des Endvermögens, wenn die Aktienpreise stetigen Semimartingaldynamiken genügen und die Strategien des Agenten Investitions- und Informationsrestriktionen unterworfen sind. Hauptaugenmerk liegt auf der stochastischen Rückwärtsgleichung (BSDE) für den dynamischen Wertprozess und auf der Übertragung von neuen Ergebnissen zu quadratischen Semimartingal-BSDEs auf das Investitionsproblem. Dieses gelingt unter der Annahme endlicher exponentiellen Momente des Mean-Variance Tradeoff und verallgemeinert frühere Resultate, die Beschränktheit fordern. Wir betrachten dabei zunächst die Beziehung zwischen den Dualitäts- und BSDE-Ansätzen zur Lösung des Problems und gehen dann über zum Studium der quadratischen Semimartingal-BSDE, wenn der Marktpreis des Risikos vom BMO-Typ ist. Wir zeigen, dass es stets ein Kontinuum verschiedener BSDE-Lösungen mit quadratisch integrierbarem Martingalteil gibt. Wir stellen dann eine neue scharfe Bedingung an geeignete dynamische exponentielle Momente vor, die die Beschränktheit der BSDE-Lösungen in einer allgemeinen Filtration garantiert. In weiterer Folge weisen wir Existenz-, Eindeutigkeits-, Stabilitäts- und Maßwechselresultate für allgemeine quadratische stetige BSDEs unter exponentiellen Momenten nach. Diese Ergebnisse verwenden wir, um das Investitionsproblem für den Fall konischer Investitionsrestriktionen zu untersuchen. Ausgehend von der Zerlegung von Elementen des dualen Gebietes erhalten wir die zugehörige BSDE und beweisen, dass der Wertprozess in einem Raum liegt, in dem Lösungen quadratischer BSDEs eindeutig sind. Als Folgerung aus dem Stabilitätsresultat für BSDEs erhalten wir die Stetigkeit der Optimierer in der Semimartingaltopologie in den Parametern des Modells. Schließlich betrachten wir das Investitionsproblem unter exponentiellen Momenten, kompakten Handelsrestriktionen und eingeschränkter Information. Hierbei benutzen wir ausschließlich BSDE-Resultate. / In this thesis we consider the problem of maximizing the power utility from terminal wealth when the stocks have continuous semimartingale dynamics and there are investment and information constraints on the agent''s strategies. The main focus is on the backward stochastic differential equation (BSDE) that encodes the dynamic value process and on transferring new results on quadratic semimartingale BSDEs to the portfolio choice problem. This is accomplished under the assumption of finite exponential moments of the mean-variance tradeoff, generalizing previous results which require boundedness. We first recall the relationship between the duality and BSDE approaches to solving the problem and then study the associated quadratic semimartingale when the market price of risk is of BMO type. We show that there is always a continuum of distinct solutions to this BSDE with square-integrable martingale part. We then provide a new sharp condition on the dynamic exponential moments of the mean-variance tradeoff which guarantees the boundedness of BSDE solutions in a general filtration. In a subsequent step we establish existence, uniqueness, stability and measure change results for general quadratic continuous BSDEs under an exponential moments condition. We use these results to study the portfolio selection problem when there are conic investment constraints. Building on a decomposition result for the elements of the so-called dual domain we derive the associated BSDE and show that the value process is contained in a specific space in which BSDE solutions are unique. A consequence of the stability result for BSDEs is then the continuity of the optimizers with respect to the input parameters of the model in the semimartingale topology. Finally, we study the optimal investment problem under exponential moments, compact constraints and restricted information. This is done by referring to BSDE results only.

<p>A survival distribution is developed for exponential two-component systems that can survive as long as at least one of the two components in the system function. It is assumed that the two components are initially independent and non-identical. If one of the two components fail (repair is impossible), the surviving component is subject to a different failure rate due to the stress caused by the failure of the other.</p> <p>In this paper, we consider such an exponential two-component system failure model when the observed failure time data are (1) complete, (2) Type-I censored, (3) Type-I censored with partial information on component failures, (4) Type-II censored and (5) Type-II censored with partial information on component failures. In these situations, we discuss the maximum likelihood estimates (MLEs) of the parameters by assuming the lifetimes to be exponentially distributed. The exact distributions (whenever possible) of the MLEs of the parameters are then derived by using the conditional moment generating function approach. Construction of confidence intervals for the model parameters are discussed by using the exact conditional distributions (when available), asymptotic distributions, and two parametric bootstrap methods. The performance of these four confidence intervals, in terms of coverage probabilities are then assessed through Monte Carlo simulation studies. Finally, some examples are presented to illustrate all the methods of inference developed here.</p> <p>In the case of Type-I and Type-II censored data, since there are no closed-form expressions for the MLEs, we present an iterative maximum likelihood estimation procedure for the determination of the MLEs of all the model parameters. We also carry out a Monte Carlo simulation study to examine the bias and variance of the MLEs.</p> <p>In the case of Type-II censored data, since the exact distributions of the MLEs depend on the data, we discuss the exact conditional confidence intervals and asymptotic confidence intervals for the unknown parameters by conditioning on the data observed.</p> / Thesis / Doctor of Philosophy (PhD)

<p>Diss. Stockholm : Handelshögskolan, 2013. Sammanfattning jämte 3 uppsatser.</p>

Submitted by Vivian Malta Nunes (vivianmalta@yahoo.com.br) on 2013-12-18T16:26:21Z No. of bitstreams: 1 Tese_Vivian_Final.pdf: 1556413 bytes, checksum: d21c4cfb4b686d356131b508247b2cc4 (MD5) / Approved for entry into archive by ÁUREA CORRÊA DA FONSECA CORRÊA DA FONSECA (aurea.fonseca@fgv.br) on 2014-01-28T17:57:42Z (GMT) No. of bitstreams: 1 Tese_Vivian_Final.pdf: 1556413 bytes, checksum: d21c4cfb4b686d356131b508247b2cc4 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2014-02-03T16:12:27Z (GMT) No. of bitstreams: 1 Tese_Vivian_Final.pdf: 1556413 bytes, checksum: d21c4cfb4b686d356131b508247b2cc4 (MD5) / Made available in DSpace on 2014-02-03T16:12:45Z (GMT). No. of bitstreams: 1 Tese_Vivian_Final.pdf: 1556413 bytes, checksum: d21c4cfb4b686d356131b508247b2cc4 (MD5) Previous issue date: 2013-06-18 / This thesis studies price-setting models and analyzes their macroeconomic im- plications. In the rst two chapters I study general models in which rms pricing decisions are a¤ected by menu costs and information costs. In Chapter 1 I estimate these models using American data on price changes, concluding that: information costs are signi cantly higher than menu costs; real data does not t into the model in which rms receive information about aggregate conditions freely but pay for idio- syncratic information. In Chapter 2 I explore the consequences of monetary shocks and disin ation announcements using the previously estimated models. I show that the degree of monetary non-neutrality is larger in an economy where part of the infor- mation is given for free. Chapter 3 is a coauthored paper with Carlos Carvalho and Antonella Tutino. We abstract from menu costs and examine a price-setting model in which rms are subject to a Shannon constraint on information ow. We calibrate the model and investigate impulse response functions to aggregate and idiosyncratic shocks. We nd that, rather than tracking aggregate and idiosyncratic conditions independently, rms prefer to process information altogether, and that leads to a faster overall price level adjustment, and thus to less real e¤ects persistence after a monetary shock. / Esta tese se dedica ao estudo de modelos de fixação de preços e suas implicações macroeconômicas. Nos primeiros dois capítulos analiso modelos em que as decisões das firmas sobre seus preços praticados levam em conta custos de menu e de informação. No Capítulo 1 eu estimo tais modelos empregando estatísticas de variações de preços dos Estados Unidos, e concluo que: os custos de informação são significativamente maiores que os custos de menu; os dados claramente favorecem o modelo em que informações sobre condições agregadas são custosas enquanto que as idiossincráticas têm custo zero. No Capítulo 2 investigo as consequências de choques monetários e anúncios de desinflação usando os modelos previamente estimados. Mostro que o grau de não-neutralidade monetária é maior no modelo em que parte da informação é grátis. O Capítulo 3 é um artigo em conjunto com Carlos Carvalho (PUC-Rio) e Antonella Tutino (Federal Reserve Bank of Dallas). No artigo examinamos um modelo de fixação de preços em que firmas estão sujeitas a uma restrição de fluxo de informação do tipo Shannon. Calibramos o modelo e estudamos funções impulso-resposta a choques idiossincráticos e agregados. Mostramos que as firmas vão preferir processar informações agregadas e idiossincráticas conjuntamente ao invés de investigá-las separadamente. Este tipo de processamento gera ajustes de preços mais frequentes, diminuindo a persistência de efeitos reais causados por choques monetários.