Advertisement

© 1998

Methods of Mathematical Finance

Benefits

  • 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

Book

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

  1. 1.Departments of Mathematics and StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

Bibliographic information

Industry Sectors
Finance, Business & Banking

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)