Die stochastische Analysis gibt Methoden zur Erfassung und Beschreibung von zufälligen numerischen Prozessen an die Hand. Die Beschreibungen hängen dabei sehr stark von der Informationsstruktur ab, die den Prozessen in Gestalt von Filtrationen zugrunde gelegt wird. Der 1. Teil der vorliegenden Arbeit handelt davon, wie sich ein Wechsel der Informationsstruktur auf das Erscheinungsbild eines stochastischen Prozesses auswirkt. Konkret geht es darum, wie sich eine Filtrationsvergrößerung auf die Semimartingalzerlegung eines Prozesses auswirkt. In dem 2. und 3. Teil der Arbeit wird die Rolle von Information im finanzmathematischen Nutzenkalkül untersucht. Im 2. Teil werden unter der Annahme, dass der maximale erwartete Nutzen eines Händlers beschränkt ist, qualitative Erkenntnisse über den Preisprozess hergeleitet. Es wird gezeigt, dass endlicher Nutzen einige strukturelle Implikationen für die intrinsische Sichtweise hat. Im 3. Teil wird quantitativ untersucht, wie sich Information auf den Nutzen auswirkt. Aus extrinsischer Sicht werden Händler mit unterschiedlichem Wissen verglichen. Falls die Präferenzen durch die logarithmische Nutzenfunktion beschrieben werden, stimmt der Nutzenzuwachs mit der gemeinsamen Information zwischen dem zusätzlichen Wissen und dem ursprünglichen Wissen überein, wobei `gemeinsame Information' im Sinne der Informationstheorie verstanden wird. / Stochastic Analysis provides methods to describe random numerical processes. The descriptions depend strongly on the underlying information structure, which is represented in terms of filtrations. The first part of this thesis deals with impacts of changes in the information structure on the appearance of a stochastic process. More precisely, it analyses the consequences of a filtration enlargement on the semimartingale decomposition of the process. The second and third part discuss the role of information in financial utility calculus. The second part is of a qualitative nature: It deals with implications of the assumption that the maximal expected utility of an investor is bounded. It is shown that finite utility implies some structure properties of the price process viewed from the intrinsic perspective. The third part is of a quantitative nature: It analyzes the impact of information on utility. From an extrinsic point of view traders with different knowledge are compared. If the preferences of the investor are described by the logarithmic utility function, then the utility increment coincides with the mutual information between the additional knowledge and the original knowledge.

Modern economic theory of self-interest alleges that in their economic relations people always behave in a way that maximises their utility. The idea whether human beings were solely self-interested has a long history as it can be seen from the writings of Greek philosophers and the Church fathers. Among Greek philosophers there were those who argued that human beings were naturally self-interested (Aristotle) and those who maintained that human beings were communal by nature (Plato, Stoics and the Pythagoreans). The later position was adopted by the Church fathers as they condemned self-interest as the sin of avarice and greed. The justification of self-interest in human and political activities was part and parcel of the economic and political early modernists, as it can be seen in the works of Mandeville, Hobbes, Hume and Adam Smith. In the writings of these thinkers, the flourishing of wealth depended on individual freedom to pursue their self-interests. In this regard, selfinterest became the sole source of motivation in the behaviour of homo economicus. A persistent motif in late modern economic discourse on self-interest is based on the idea that people think and act on the basis of that which is to their self-interest. It is mainly for this reason that late modern economic thinkers maintain that society would prosper when people are left alone to pursue their self-interests. Late modern economic theory of utility maximisation alleges that individuals act only after calculating costs and benefits. The argument of this thesis, based on the commonalities between African humanism and process philosophical anthropology, is that self-interest is antithetical to communal life as advocated in the ethic of Ubuntu. One who acts solely on the basis of maximising his or her utility would inevitably deprive others of a humane existence. A holistic metaphysical outlook based on the relatedness and interrelatedness of everything that exists as we find it in African humanism and process philosophical anthropology implies that the individual exists in internal relations with everything else. We should go beyond selfinterest by giving primacy to a holistic ethic. / Systematic Theology & Theological Ethics / D. Div. (Theological Ethics)

Dans cette thèse nous considérons le problème de la maximisation d’utilité et de la formation des prix d’indifférence pour les modèles semimartingales exponentiels dépendant d’un facteur aléatoire ξ. L’enjeu est de résoudre le problème des prix d’indifférence en utilisant le grossissement de l’espace et de la filtration. Nous réduisons le problème de maximisation dans la filtration élargie au problème conditionnel, sachant {ξ = v}, que nous résolvons en utilisant une approche duale. Pour HARA-utilités nous introduisons les informations telles que les entropies relatives et les intégrales de type Hellinger, ainsi que les processus d’information correspondants, enfin d’exprimer, via ces processus, l’utilité maximal. En particulier, nous étudions les modèles de Lévy exponentiels, où les processus d’information sont déterministes ce que simplifie considèrablement les calculs des prix d’indiffrence. Enfin, nous appliquons les rèsultats au modèle du mouvement brownien géométrique et au modèle de diffusion-sauts qui inclut le mouvement brownien et les processus de Poisson. Dans les cas d’utilité logarithmique, de puissance et exponentielle, nous fournissons les formules explicites des informations, et puis, en utilisant les méthodes numériques, nous résolvons les équations pour obtenir les prix d’indifférence en cas de vente d’une option européenne. / This thesis explores the utility maximisation problem and indifference pricing for exponential semimartingale models depending on a random factor ξ. The main idea to solve indifference pricing problem consists in the enlargement of the space and filtration. We reduce the maximization problem on the enlarged filtration to the conditional one, given {ξ = v}, which we solve using dual approach. For HARA-utilities we introduce the information quantities such that the relative entropies, Hellinger type integrals, and the corresponding information processes, and we express the maximal utility via these processes. As a particular case, we study exponential Levy models, where the information processes are deterministic and this fact simplify very much indifference price calculus. Finally, we apply the results to Geometric Brownian motion model and jump-diffusion model which incorporates Brownian motion and Poisson process. In the cases of logarithmic, power and exponential utilities, we provide the explicit formulae of information quantities and using the numerical methods we solve the equations for the seller’s and buyer’s indifference prices of European put option.

Modern economic theory of self-interest alleges that in their economic relations people always behave in a way that maximises their utility. The idea whether human beings were solely self-interested has a long history as it can be seen from the writings of Greek philosophers and the Church fathers. Among Greek philosophers there were those who argued that human beings were naturally self-interested (Aristotle) and those who maintained that human beings were communal by nature (Plato, Stoics and the Pythagoreans). The later position was adopted by the Church fathers as they condemned self-interest as the sin of avarice and greed. The justification of self-interest in human and political activities was part and parcel of the economic and political early modernists, as it can be seen in the works of Mandeville, Hobbes, Hume and Adam Smith. In the writings of these thinkers, the flourishing of wealth depended on individual freedom to pursue their self-interests. In this regard, selfinterest became the sole source of motivation in the behaviour of homo economicus. A persistent motif in late modern economic discourse on self-interest is based on the idea that people think and act on the basis of that which is to their self-interest. It is mainly for this reason that late modern economic thinkers maintain that society would prosper when people are left alone to pursue their self-interests. Late modern economic theory of utility maximisation alleges that individuals act only after calculating costs and benefits. The argument of this thesis, based on the commonalities between African humanism and process philosophical anthropology, is that self-interest is antithetical to communal life as advocated in the ethic of Ubuntu. One who acts solely on the basis of maximising his or her utility would inevitably deprive others of a humane existence. A holistic metaphysical outlook based on the relatedness and interrelatedness of everything that exists as we find it in African humanism and process philosophical anthropology implies that the individual exists in internal relations with everything else. We should go beyond selfinterest by giving primacy to a holistic ethic. / Philosophy, Practical and Systematic Theology / D. Div. (Theological Ethics)