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Authors:

Rong Situ

Rong Situ

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Derivation of Ito’s formulas, Girsanov’s theorems and martingale representation theorem for stochastic DEs with jumps
Applications to population control
Reflecting stochastic DE technique
Applications to the stock market. (Backward stochastic DE approach)
Derivation of Black-Scholes formula for market with and without jumps
Non-linear filtering problems with jumps

Part of the book series: Mathematical and Analytical Techniques with Applications to Engineering (MATE)

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Table of contents (12 chapters)

Front Matter

Pages i-xx

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Stochastic Differential Equations with Jumps in Rd
1. Martingale Theory and the Stochastic Integral for Point Processes
  
  Pages 3-38
2. Brownian Motion, Stochastic Integral and Ito's Formula
  
  Pages 39-74
3. Stochastic Differential Equations
  
  Pages 75-101
4. Some Useful Tools in Stochastic Differential Equations
  
  Pages 103-137
5. Stochastic Differential Equations with Non-Lipschitzian Coefficients
  
  Pages 139-160
Applications
1. How to Use the Stochastic Calculus to Solve SDE
  
  Pages 163-168
2. Linear and Non-linear Filtering
  
  Pages 169-204
3. Option Pricing in a Financial Market and BSDE
  
  Pages 205-275
4. Optimal Consumption by H-J-B Equation and Lagrange Method
  
  Pages 277-290
5. Comparison Theorem and Stochastic Pathwise Control
  
  Pages 291-327
6. Stochastic Population Control and Reflecting SDE
  
  Pages 329-376
7. Maximum Principle for Stochastic Systems with Jumps
  
  Pages 377-387
Back Matter

Pages 389-434

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Keywords

About this book

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

Bibliographic Information

Book Title: Theory of Stochastic Differential Equations with Jumps and Applications
Book Subtitle: Mathematical and Analytical Techniques with Applications to Engineering
Authors: Rong Situ
Series Title: Mathematical and Analytical Techniques with Applications to Engineering
DOI: https://doi.org/10.1007/b106901
Publisher: Springer New York, NY
eBook Packages: Engineering, Engineering (R0)
Hardcover ISBN: 978-0-387-25083-0Published: 20 April 2005
Softcover ISBN: 978-1-4419-3771-1Published: 08 December 2010
eBook ISBN: 978-0-387-25175-2Published: 06 May 2006
Series ISSN: 1559-7458
Series E-ISSN: 1559-7466
Edition Number: 1
Number of Pages: XX, 434
Topics: Mathematical and Computational Engineering, Analysis, Probability Theory and Stochastic Processes, Applications of Mathematics, Theoretical, Mathematical and Computational Physics, Engineering Fluid Dynamics

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Theory of Stochastic Differential Equations with Jumps and Applications

Overview

Access this book

Other ways to access

Table of contents (12 chapters)

Front Matter

Stochastic Differential Equations with Jumps in Rd

Applications

Back Matter

Keywords

About this book

Bibliographic Information

Publish with us

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