Portfolio Optimizations in Incomplete Financial Markets

1. Auflage 2004
ISBN: 978-88-7642-141-9
Verlag: Scuola Normale Superiore

Buch, Englisch, 65 Seiten, Format (B × H): 170 mm x 240 mm

Reihe: Publications of the Scuola Normale Superiore

These Lecture Notes are based on a course given in June 2001 at the Cattedra Galileiana of Scuola Normale Superiore di Pisa. The course consisted of a short introduction into the basic concepts of Mathematical Finance, focusing on the notion of “no arbitrage”, and subsequently applying these concepts to portfolio optimization. To avoid technical difficulties I mainly dealt with the situation where the underlying probability space is finite and only sketched the difficulties arising in the general case. We then pass to the scheme of utility optimisation for general semi-martingale models. Some topics of this course are not standard: for example, in the treatment of the general existence theorem for the optimal portfolio, we give a direct proof which is not relying on duality theory. Similarly, the treatment of the asymptotic elasticity of utility functions and a related counter-example are original to these notes.

Zielgruppe

Research

Autoren/Hrsg.

Schachermayer, Walter

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle