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Stochastic Calculus and Financial Applications

  • J. Michael Steele

Part of the Applications of Mathematics book series (SMAP, volume 45)

Table of contents

  1. Front Matter
    Pages i-ix
  2. J. Michael Steele
    Pages 1-10
  3. J. Michael Steele
    Pages 11-28
  4. J. Michael Steele
    Pages 29-42
  5. J. Michael Steele
    Pages 43-60
  6. J. Michael Steele
    Pages 61-78
  7. J. Michael Steele
    Pages 79-94
  8. J. Michael Steele
    Pages 95-109
  9. J. Michael Steele
    Pages 111-135
  10. J. Michael Steele
    Pages 137-151
  11. J. Michael Steele
    Pages 153-168
  12. J. Michael Steele
    Pages 169-190
  13. J. Michael Steele
    Pages 191-212
  14. J. Michael Steele
    Pages 213-231
  15. J. Michael Steele
    Pages 233-261
  16. J. Michael Steele
    Pages 263-275
  17. Back Matter
    Pages 277-301

About this book

Introduction

This book is designed for students who want to develop professional skill in stochastic calculus and its application to problems in finance. The Wharton School course that forms the basis for this book is designed for energetic students who have had some experience with probability and statistics but have not had ad­ vanced courses in stochastic processes. Although the course assumes only a modest background, it moves quickly, and in the end, students can expect to have tools that are deep enough and rich enough to be relied on throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more de­ manding development of continuous-time stochastic processes, especially Brownian motion. The construction of Brownian motion is given in detail, and enough mate­ rial on the subtle nature of Brownian paths is developed for the student to evolve a good sense of when intuition can be trusted and when it cannot. The course then takes up the Ito integral in earnest. The development of stochastic integration aims to be careful and complete without being pedantic.

Keywords

Stochastic Differential Equations Stochastic Processes Stochastic calculus Uniform integrability Variance calculus statistics

Authors and affiliations

  • J. Michael Steele
    • 1
  1. 1.The Wharton School, Department of StatisticsUniversity of PennsylvaniaPhiladelphiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9305-4
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2862-7
  • Online ISBN 978-1-4684-9305-4
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site