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Methods of Mathematical Finance

  • Ioannis Karatzas
  • Steven E. Shreve

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 39)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ioannis Karatzas, Steven E. Shreve
    Pages 1-35
  3. Ioannis Karatzas, Steven E. Shreve
    Pages 36-87
  4. Ioannis Karatzas, Steven E. Shreve
    Pages 88-158
  5. Ioannis Karatzas, Steven E. Shreve
    Pages 159-198
  6. Ioannis Karatzas, Steven E. Shreve
    Pages 199-259
  7. Ioannis Karatzas, Steven E. Shreve
    Pages 260-321
  8. Back Matter
    Pages 323-415

About this book

Introduction

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. 

Keywords

Brownian motion Stochastic calculus agents equilibrium finance incomplete markets mathematical finance mathematics valuation

Authors and affiliations

  • Ioannis Karatzas
    • 1
  • Steven E. Shreve
    • 2
  1. 1.Departments of Mathematics and StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-6845-9
  • Copyright Information Springer-Verlag New York 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-6814-5
  • Online ISBN 978-1-4939-6845-9
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • Buy this book on publisher's site