Stochastic Differential Equations : An Introduction with Applications / by Bernt Oksendal.

Format:

Book

Author/Creator:

Oksendal, Bernt., Author.

Series:

Universitext, 2191-6675

Language:

English

Subjects (All):

Probabilities.

Differential equations.

Mathematical physics.

System theory.

Control theory.

Mathematical optimization.

Calculus of variations.

Probability Theory.

Differential Equations.

Theoretical, Mathematical and Computational Physics.

Systems Theory, Control.

Calculus of Variations and Optimization.

Local Subjects:

Probability Theory.

Differential Equations.

Theoretical, Mathematical and Computational Physics.

Systems Theory, Control.

Calculus of Variations and Optimization.

Physical Description:

1 online resource (XIX, 324 p.)

Edition:

5th ed. 1998.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.

Language Note:

English

Summary:

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.

Contents:

1. Introduction

2. Some Mathematical Preliminaries

3. Ito Integrals

4. The Ito Formula and the Martingale Representation Theorem

5. Stochastic Differential Equations

6. The Filtering Problem

7. Diffusions: Basic Properties

8. Other Topics in Diffusion Theory

9. Applications to Boundary Value Problems

10. Application to Optimal Stopping

11. Application to Stochastic Control

12. Application to Mathematical Finance

Appendix A: Normal Random Variables

Appendix B: Conditional Expectation

Appendix C: Uniform Integrability and Martingale Convergence

Appendix D: An Approximation Result

Solutions and Additional Hints to Some of the Exercises

References

List of Frequently Used Notation and Symbols.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

3-662-03620-7