Probability Theory and Stochastic Modelling

Methods of Mathematical Finance

Authors: Karatzas, Ioannis, Shreve, Steven

  • 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

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

"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)

  • A Brownian Model of Financial Markets

    Karatzas, Ioannis (et al.)

    Pages 1-35

  • Contingent Claim Valuation in a Complete Market

    Karatzas, Ioannis (et al.)

    Pages 36-87

  • Single-Agent Consumption and Investment

    Karatzas, Ioannis (et al.)

    Pages 88-158

  • Equilibrium in a Complete Market

    Karatzas, Ioannis (et al.)

    Pages 159-198

  • Contingent Claims in Incomplete Markets

    Karatzas, Ioannis (et al.)

    Pages 199-259

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4939-6845-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4939-6814-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Methods of Mathematical Finance
Authors
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 and Tables
20 b/w illustrations
Additional Information
1st edition 1998; Corrected 4th printing 2016
Topics