© 2013

Optimal Investment


  • Presents the main methods for solving stochastic optimal control problems arising in finance

  • Through a large number of worked problems, illustrates how to use a combination of analytic and numerical techniques to actually find a solution even when none is available in closed form

  • Critiques the usefulness of theory in the light of stylized facts of asset return


Part of the SpringerBriefs in Quantitative Finance book series (BRIEFFINANCE)

Table of contents

  1. Front Matter
    Pages i-x
  2. L. C. G. Rogers
    Pages 1-28
  3. L. C. G. Rogers
    Pages 29-113
  4. L. C. G. Rogers
    Pages 115-135
  5. L. C. G. Rogers
    Pages 137-150
  6. Back Matter
    Pages 151-156

About this book


Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics.
Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques
that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.


91G10, 91G70, 91G80, 49L20, 65K15 Hamilton-jacobi-Bellman equation Ito's formula Optimal investment asset returns martingale

Authors and affiliations

  1. 1.Dept. Pure Mathematics &University of Cambridge Centre for Mathematical SciencesCambridgeUnited Kingdom

Bibliographic information

Industry Sectors
Finance, Business & Banking


From the book reviews:

“This short book would be an excellent supplementary text for a course in quantitative finance or useful to researchers or practitioners looking for an overview of one of the foundations of modern quantitative finance.” (IEEE Control Systems Magazine, October, 2013)

“This book first focuses on the classical Merton problems and presents a range of techniques for solving optimal investment/consumption problems. … I really enjoyed reading this book. … it would be very helpful to students and researchers who are interested in financial engineering, corporate finance and asset pricing, and it would be worth keeping the book on their shelves.” (Zhaojun Yang, Mathematical Reviews, September, 2013)