© 2002

Stochastic Portfolio Theory


Part of the Applications of Mathematics book series (SMAP, volume 48)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. E. Robert Fernholz
    Pages 1-24
  3. E. Robert Fernholz
    Pages 25-42
  4. E. Robert Fernholz
    Pages 43-67
  5. E. Robert Fernholz
    Pages 69-92
  6. E. Robert Fernholz
    Pages 93-118
  7. E. Robert Fernholz
    Pages 119-142
  8. E. Robert Fernholz
    Pages 143-164
  9. Back Matter
    Pages 165-178

About this book


Stochastic portfolio theory is a novel mathematical framework for constructing portfolios, analyzing the behavior of portfolios, and understanding the structure of equity markets. This new theory is descriptive as opposed to normative, and is consistent with the observed behavior and structure of actual markets. Stochastic portfolio theory is important for both academics and practitioners, for it includes theoretical results of central importance to modern mathematical finance, a well as techniques that have been successfully applied to the management of actual stock portfolios for institutional investors. Of particular interest are the logarithmic representation stock prices for portfolio optimization; portfolio generating functions and the existence of arbitrage; and the use of ranked market weight processes for analyzing equity market structure.
For academics, the book offers a fresh view of equity market structure as well as a coherent exposition of portfolio generating functions. Included are many open research problems related to these topics, some of which are probably appropriate for graduate dissertations.
For practioners, the book offers a comprehensive exposition of the logarithmic model for portfolio optimization, as well as new methods for performance analysis and asset allocation.
E. Robert Fernholz is Chief Investment Officer of INTECH, an institutional equity manager. Previously, Dr. Fernholz taught mathematics and statistics at Princeton University and the City University of New York.


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Authors and affiliations

  1. 1.INTECHPrincetonUSA

Bibliographic information

  • Book Title Stochastic Portfolio Theory
  • Authors E. Robert Fernholz
  • Series Title Applications of Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-95405-9
  • Softcover ISBN 978-1-4419-2987-7
  • eBook ISBN 978-1-4757-3699-1
  • Series ISSN 0172-4568
  • Edition Number 1
  • Number of Pages XIV, 178
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Finance, general
    Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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From the reviews:


"We recommend this monograph to all researchers and graduate students in mathematical finance; it is easy to read, self-contained, not boring at all, and with lots of ideas for further research."

"The monograph introduces stochastic portfolio theory, a novel mathematical framework for analyzing portfolio behavior and equity market structure, and which is intended for investment professionals and students of mathematical finance. … We recommend this monograph to all researchers and graduate students in mathematical finance; it is easy to read, self-contained, not boring at all, and with lots of ideas for further research." (Gheorghe Stoica, Mathematical Reviews, 2003 a)

"This book develops a descriptive theory of portfolios in financial markets. … It can be used as a theoretical tool to provide insight into questions of market equilibrium and arbitrage, and to construct portfolios with controlled behaviour. In practice, it can be applied to portfolio optimization and performance analysis, and the tools developed will be useful for these purposes. … it will help to understand why certain investment strategies produce certain results … ." (Martin Schweizer, Zentralblatt MATH, Vol. 1049, 2004)