- Topics are treated for the first time in a unified manner
- Contains an extensive set of references and notes
- Provides an exhaustive and up-to-date treatment of portfolio optimization and valuation problems under constraints
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- About this book
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This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to the study of complete market equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text.
This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.
- Reviews
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"The book under review deals with the applications of stochastic analysis and optimal control theory to various problems arising in modern mathematical finance. In contrast to several other books on mathematical finance which appeared in recent years, this book deals not only with the so-called partial equilibrium approach (i.e., the arbitrage pricing of European and American contingent claims) but also with the general equilibrium approach (i.e., with the equilibrium specification of prices of primary assets). A major part of the book is devoted to solving valuation and portfolio optimization problems under market imperfections, such as market incompleteness and portfolio constraints. ... Undoubtedly, the book constitutes a valuable research-level text which should be consulted by anyone interested in the area. Unlike other currently available monographs, it provides an exhaustive and up-to-date treatment of portfolio optimization and valuation problems under constraints. It is also quite suitable as a textbook for an advanced course on mathematical finance." (Marek RutKowski, Mathematical Reviews)
- Table of contents (6 chapters)
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A Brownian Model of Financial Markets
Pages 1-35
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Contingent Claim Valuation in a Complete Market
Pages 36-87
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Single-Agent Consumption and Investment
Pages 88-158
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Equilibrium in a Complete Market
Pages 159-198
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Contingent Claims in Incomplete Markets
Pages 199-259
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Methods of Mathematical Finance
- Authors
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- Ioannis Karatzas
- Steven Shreve
- Series Title
- Probability Theory and Stochastic Modelling
- Series Volume
- 39
- Copyright
- 1998
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer-Verlag New York
- eBook ISBN
- 978-1-4939-6845-9
- DOI
- 10.1007/978-1-4939-6845-9
- Hardcover ISBN
- 978-1-4939-6814-5
- Series ISSN
- 2199-3130
- Edition Number
- 1
- Number of Pages
- XV, 415
- Number of Illustrations
- 20 b/w illustrations
- Additional Information
- 1st edition 1998; Corrected 4th printing 2016
- Topics
