Stochastic Finance

An Introduction in Discrete Time
3rd revidierte and extend. Auflage 2011
ISBN: 978-3-11-021804-6
Verlag: De Gruyter

Buch, Englisch, 544 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 932 g

Reihe: De Gruyter Textbook

This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This third revised and extended edition now contains more than one hundred exercises. It also includes new material on risk measures and the related issue of model uncertainty, in particular a new chapter on dynamic risk measures and new sections on robust utility maximization and on efficient hedging with convex risk measures.

Zielgruppe

Graduate Students of Mathematics, Researchers, Practitioners; Academic Libraries

Autoren/Hrsg.

Schied, Alexander

Föllmer, Hans

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik

Inhaltsverzeichnis

Frontmatter

Preface to the third edition

Preface to the second edition

Preface to the first edition

Contents

I Mathematical finance in one period

1 Arbitrage theory
2 Preferences
3 Optimality and equilibrium
4 Monetary measures of risk

II Dynamic hedging

5 Dynamic arbitrage theory
6 American contingent claims
7 Superhedging
8 Efficient hedging
9 Hedging under constraints
10 Minimizing the hedging error
11 Dynamic risk measures

Appendix

Notes

Bibliography

List of symbols

Index

Über Autor(innen)

Föllmer, Hans
Hans Föllmer, Humboldt-Universität zu Berlin

Schied, Alexander
Alexander Schied, Universität Mannheim.

Hans Föllmer, Humboldt-Universität zu Berlin; Alexander Schied, Universität Mannheim.