Information and semimartingales [Elektronische Ressource] / von Stefan Ankirchner

Stefan Ankirchner

Sujets

• Mathematics

Informations

• Publié par: humboldt-universitat_zu_berlin
• Publié le: 01 janvier 2005
• Nombre de lectures: 8
• Langue: English

Extrait

Information and Semimartingales
DISSERTATION
zur Erlangung des akademischen Grades
doctor rerum naturalium
(Dr. rer. nat.)
im Fach Mathematik
eingereicht an der
Mathematisch-Naturwissenschaftlichen Fakultat II
Humboldt-Universitat zu Berlin
von
Herr Dipl.-Math. Stefan Ankirchner
geboren am 13.03.1976 in Muhldorf am Inn
Prasident der Humboldt-Universitat zu Berlin:
Prof. Dr. Jurgen Mlynek
Dekan der Mathematisch-Naturwissenschaftlichen Fakultat II:
Prof. Dr. Uwe Kuchler
Gutachter:
1. Prof. Dr. Peter Imkeller
2. Prof. Dr. Hans Follmer
3. Prof. Dr. Arturo Kohatsu-Higa
eingereicht am: 22. Marz 2005
Tag der mundlichen Prufung: 1. Juli 2005Abstract
Stochastic Analysis provides methods to describe random numerical pro-
cesses. Thedescriptionsdependstronglyontheunderlyinginformationstruc-
ture, which is represented in terms of ltrations. The rst part of this thesis
deals with impacts of changes in the information structure on the appear-
ance of a stochastic process. More precisely, it analyses the consequences of
a ltration enlargement on the semimartingale decomposition of the process.
From the martingale part a drift has to be subtracted in order to obtain a
martingale in the enlarged ltration. Methods are given how one can com-
pute and analyze this correcting drift.
The second and third part discuss the role of information in nancial
utility calculus: In the framework of the general semimartingale model of
nancial markets the link between information and utility is analyzed.
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 nite utility implies some structure properties of the price
processviewedfromtheintrinsicperspective: Atrstitfollowsthattheprice
is a semimartingale. Moreover, one can show for continuous processes that
the bounded variation part in the semimartingale decomposition is nicely
controlled by the martingale part and does not explode. Thus the second
part justi