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Stochastic Differential Equations

An Introduction with Applications

  • Bernt Øksendal

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Bernt Øksendal
    Pages 1-5
  3. Bernt Øksendal
    Pages 7-19
  4. Bernt Øksendal
    Pages 21-42
  5. Bernt Øksendal
    Pages 61-78
  6. Bernt Øksendal
    Pages 79-106
  7. Bernt Øksendal
    Pages 107-130
  8. Bernt Øksendal
    Pages 131-165
  9. Bernt Øksendal
    Pages 167-194
  10. Bernt Øksendal
    Pages 195-223
  11. Bernt Øksendal
    Pages 225-248
  12. Bernt Øksendal
    Pages 249-288
  13. Back Matter
    Pages 289-324

About this book

Introduction

The main new feature of the fifth edition is the addition of a new chapter, Chapter 12, on applications to mathematical finance. I found it natural to include this material as another major application of stochastic analysis, in view of the amazing development in this field during the last 10-20 years. Moreover, the close contact between the theoretical achievements and the applications in this area is striking. For example, today very few firms (if any) trade with options without consulting the Black & Scholes formula! The first 11 chapters of the book are not much changed from the previous edition, but I have continued my efforts to improve the presentation through­ out and correct errors and misprints. Some new exercises have been added. Moreover, to facilitate the use of the book each chapter has been divided into subsections. If one doesn't want (or doesn't have time) to cover all the chapters, then one can compose a course by choosing subsections from the chapters. The chart below indicates what material depends on which sections. Chapter 6 Chapter IO Chapter 12 For example, to cover the first two sections of the new chapter 12 it is recom­ mended that one (at least) covers Chapters 1-5, Chapter 7 and Section 8.6. VIII Chapter 10, and hence Section 9.1, are necessary additional background for Section 12.3, in particular for the subsection on American options.

Keywords

Boundary value problem Differential Equations Equations Martingale Optimal Filtering Random variable Stochastic calculus Un application applications filtering problem filtering theory mathematical finance optimal stopping stochastic analysis

Authors and affiliations

  • Bernt Øksendal
    • 1
  1. 1.Department of MathematicsUniversity of OsloOsloNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03620-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63720-2
  • Online ISBN 978-3-662-03620-4
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site