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  • Textbook
  • © 1998

Stochastic Differential Equations

An Introduction with Applications

Authors:

  1. Bernt Øksendal

    1. Department of Mathematics, University of Oslo, Oslo, Norway

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  • This well-established textbook on stochastic differential equations has turned out to be very useful to non-specialists of the subject and has sold steadily in 4 editions, both in the EU and US market

Part of the book series: Universitext (UTX)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XIX
    PDF

  2. Introduction

    • Bernt Øksendal
    Pages 1-5

  3. Some Mathematical Preliminaries

    • Bernt Øksendal
    Pages 7-19

  4. Ito Integrals

    • Bernt Øksendal
    Pages 21-42

  6. Stochastic Differential Equations

    • Bernt Øksendal
    Pages 61-78

  7. The Filtering Problem

    • Bernt Øksendal
    Pages 79-106

  8. Diffusions: Basic Properties

    • Bernt Øksendal
    Pages 107-130

  9. Other Topics in Diffusion Theory

    • Bernt Øksendal
    Pages 131-165

  10. Applications to Boundary Value Problems

    • Bernt Øksendal
    Pages 167-194

  11. Application to Optimal Stopping

    • Bernt Øksendal
    Pages 195-223

  12. Application to Stochastic Control

    • Bernt Øksendal
    Pages 225-248

  13. Application to Mathematical Finance

    • Bernt Øksendal
    Pages 249-288

  14. Back Matter

    Pages 289-324
    PDF
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About this book

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.
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Keywords

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Authors and Affiliations

  • Department of Mathematics, University of Oslo, Oslo, Norway

    Bernt Øksendal

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Bibliographic Information

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eBook USD 74.99
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  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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