Gegenstand der vorliegenden Dissertation sind stochastische Kontrollprobleme, denen sich Agenten im Zusammenhang mit Entscheidungen auf Finanzmärkten gegenübersehen. Der erste Teil der Arbeit behandelt die Maximierung des erwarteten Nutzens des Endvermögens eines Finanzmarktinvestors. Für den Investor ist eine Beschreibung der optimalen Handelsstrategie, die zur numerischen Approximation geeignet ist sowie eine Stabilitätsanalyse der optimalen Handelsstrategie bzgl. kleinerer Fehlspezifikationen in Nutzenfunktion und Anfangsvermögen, von höchstem Interesse. In stetigen Marktmodellen beweisen wir Stabilitätsresultate für die optimale Handeslsstrategie in geeigneten Topologien. Für hinreichend differenzierbare Nutzenfunktionen und zeitstetige Marktmodelle erhalten wir eine Beschreibung der optimalen Handelsstrategie durch die Lösung eines Systems von stochastischen Vorwärts-Rückwärts-Differentialgleichungen (FBSDEs). Der zweite Teil der Arbeit beschäftigt sich mit optimalen Stopproblemen für einen Agenten, dessen Ertragsprozess von einem Ausfallsereignis abhängt. Unser Hauptinteresse gilt der Beschreibung der Lösungen vor und nach dem Ausfallsereignis und damit dem besseren Verständnis des Verhaltens des Agenten bei Auftreten eines Ausfallsereignisses. Wir zeigen wie sich das optimale Stopproblem in zwei einzelne Teilprobleme zerlegen lässt: eines, für das der zugrunde liegende Informationsfluss das Ausfallereignis nicht beinhaltet, und eines, in welchem der Informationsfluss das Ausfallereignis berücksichtigt. Aufbauend auf der Zerlegung des Stopproblems und der Verbindung zwischen der Optimalen Stoptheorie und der Theorie von reflektierenden stochastischen Rückwärts-Differentialgleichungen (RBSDEs), leiten wir einen entsprechenden Zerlegungsansatz her, um RBSDEs mit genau einem Sprung zu lösen. Wir beweisen neue Existenz- und Eindeutigkeitsresultate von RBSDEs mit quadratischem Wachstum. / This thesis studies stochastic control problems faced by agents in financial markets when making decisions. The first part focuses on the maximization of expected utility from terminal wealth for an investor trading in a financial market. Of utmost concern to the investor is a description of optimal trading strategy that is amenable to numerical approximation, and the stability analysis of the optimal trading strategy w.r.t. "small" misspecification in his utility function and initial capital. In the setting of a continuous market model, we prove stability results for the optimal wealth process in the Emery topology and the uniform topology on semimartingales, and stability results for the optimal trading strategy in suitable topologies. For sufficiently differentiable utility functions, we obtain a description of the optimal trading strategy in terms of the solution of a system of forward-backward stochastic differential equations (FBSDEs). The second part of the thesis deals with the optimal stopping problem for an agent with a reward process exposed to a default event. Our main concern is to give a description of the solutions before and after the default event and thereby better understand the behavior of the agent in the presence of default. We show how the stopping problem can be decomposed into two individual stopping problems: one with information flow for which the default event is not visible, and another one with information flow which captures the default event. We build on the decomposition of the optimal stopping problem, and the link between the theories of optimal stopping and reflected backward stochastic differential equations (RBSDEs) to derive a corresponding decomposition approach to solve RBSDEs with a single jump. This decomposition allows us to establish existence and uniqueness results for RBSDEs with drivers of quadratic growth.

Submitted by Paulo César Coimbra Lisbôa (pc.coimbra@gmail.com) on 2010-11-11T01:39:34Z No. of bitstreams: 1 PhD_Thesis_Coimbra_v1.pdf: 516617 bytes, checksum: c44a6f3efb7c504da91a6f20e0a95b3f (MD5) / Rejected by Andrea Virginio Machado(andrea.machado@fgv.br), reason: Conforme conversamos, peço fazer a alteração para acesso livre. Andrea on 2010-11-11T14:03:11Z (GMT) / Submitted by Paulo César Coimbra Lisbôa (pc.coimbra@gmail.com) on 2010-11-11T14:17:27Z No. of bitstreams: 1 PhD_Thesis_Coimbra_v1.pdf: 516617 bytes, checksum: c44a6f3efb7c504da91a6f20e0a95b3f (MD5) / Approved for entry into archive by Andrea Virginio Machado(andrea.machado@fgv.br) on 2010-11-16T11:21:16Z (GMT) No. of bitstreams: 1 PhD_Thesis_Coimbra_v1.pdf: 516617 bytes, checksum: c44a6f3efb7c504da91a6f20e0a95b3f (MD5) / Made available in DSpace on 2010-11-17T10:49:20Z (GMT). No. of bitstreams: 1 PhD_Thesis_Coimbra_v1.pdf: 516617 bytes, checksum: c44a6f3efb7c504da91a6f20e0a95b3f (MD5) Previous issue date: 2009-11-30 / Contaminação da confiança é um caso especial de incerteza Knightiana ou ambiguidade na qual o tomador de decisões está diante de não apenas uma única distribuição de probabilidades, mas sim de um conjunto de distribuições de probabilidades. A primeira parte desta tese tem o propósito de fornecer uma caracterização da contaminação da confiança e então apresentar um conjunto de axiomas comportamentais simples sob os quais as preferências de um tomador de decisões é representada pela utilidade esperada de Choquet com contaminação da confiança. A segunda parte desta tese apresenta duas aplicações econômicas de contaminação da confiança: a primeira delas generaliza o teorema de existência de equilíbrio de Nash de Dow e Werlang (o que permite apresentar uma solução explícita para o paradoxo segundo o qual os jogadores de um jogo do dilema dos prisioneiros com um número infinito de repetições não agem de acordo com o esperado pelo procedimento da indução retroativa) e a outra estuda o impacto da contaminação da confiança na escolha de portfolio. / Contamination of confidence is a special case of Knightian uncertainty or ambiguity in which the decision maker faces not simple probability measure but a set of probability measures. The first part of this thesis has the purpose to provide a characterization of the contamination of confidence and then present a simple set of behavioral axioms under which the decision maker’s preference is represented by the Choquet expected utility with contamination of confidence. The second part of this thesis presents two economic applications of the contamination of confidence: the first of them generalizes Dow and Werlang’s existence Theorem of Nash equilibrium under uncertainty (which enables to present an explicit solution to the paradox on which players in a finitely repeated prisoners’ dilemma breaks down backward induction) and the other studies the impact of the contamination of confidence in the portfolio choice.