The series De Gruyter Studies in Mathematics was founded in 1982 by the late Professor Heinz Bauer and Professor Peter Gabriel.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.
The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level.
The series De Gruyter Studies in Mathematics is indexed in MathSciNet (Mathematical Reviews) and Scopus.
Editor-in-Chief
Guozhen Lu, University of Connecticut, USA
Editorial Board
Carstensen Carsten, Humboldt-Universitat zu Berlin, Germany
Gavril Farkas, Humboldt-Universitat zu Berlin, Germany
Nicola Fusco, Università di Napoli "Federico II", Italy
Fritz Gesztesy, Baylor University, USA
Zenghu Li, Beijing Normal University, China
Karl-Hermann Neeb, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
René L. Schilling, Technische Universität Dresden, Germany
Volkmar Welker, Philipps-Universität Marburg, Germany
Please submit book proposals to Guozhen Lu
Autorentext
Hans Föllmer is Professor for Mathematics at the Humboldt University in Berlin, Germany.
Alexander Schied is Professor at the Institute for Mathematics of the Technical University Berlin, Germany.
Klappentext
This book is an introduction to financial mathematics. The first part of the book studies a simple one-period model which 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 risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Such models are typically incomplete: They involve intrinsic risks which cannot be hedged away completely. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. In addition to many corrections and improvements, this second edition contains several new sections, including a systematic discussion of law-invariant risk measures and of the connections between American options, superhedging, and dynamic risk measures.
Zusammenfassung
This book is an introduction to financial mathematics.
The first part of the book studies a simple one-period model which 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 risk.
In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Such models are typically incomplete: They involve intrinsic risks which cannot be hedged away completely. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk.
In addition to many corrections and improvements, this second edition contains several new sections, including a systematic discussion of law-invariant risk measures and of the connections between American options, superhedging, and dynamic risk measures.