Portfolio Theory and Arbitrage: A Course in Mathematical Finance (Graduate Studies in Mathematics) - Softcover

Ioannis Karatzas (author) & Constantinos Kardaras (author)

Softcover

ISBN 10: 1470465981 ISBN 13: 9781470465988

Publisher: American Mathematical Society, 2022

Synopsis

This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called ""Kelly"" or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization.

The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.

About this title

About the Author

Ioannis Karatzas, Columbia University, New York, NY.

Constantinos Kardaras, London School of Economics and Political Science, UK.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 1470465981
• ISBN 13: 9781470465988
• Binding: Paperback
• Number of pages: 277