Overview
- 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
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 39)
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Table of contents (6 chapters)
Keywords
About this book
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. Thechapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.The present corrected printing includes, besides other minor corrections, an important correction of Theorem 6.4 and a simplification of the proof of Lemma 6.5.
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
"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)
Authors and Affiliations
Bibliographic Information
Book Title: Methods of Mathematical Finance
Authors: Ioannis Karatzas, Steven E. Shreve
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-1-4939-6845-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 1998
Hardcover ISBN: 978-1-4939-6814-5Published: 30 December 2016
eBook ISBN: 978-1-4939-6845-9Published: 10 January 2017
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
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: Quantitative Finance, Probability Theory and Stochastic Processes, Economic Theory/Quantitative Economics/Mathematical Methods