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Theory of Stochastic Differential Equations with Jumps and Applications

Mathematical and Analytical Techniques with Applications to Engineering

  • Authors
  • Rong Situ

About this book

Introduction

This book is written for people who are interested in stochastic differential equations (SDEs) and their applications. It shows how to introduce and define the Ito integrals, to establish Ito’s differential rule (the so-called Ito formula), to solve the SDEs, and to establish Girsanov’s theorem and obtain weak solutions of SDEs. It also shows how to solve the filtering problem, to establish the martingale representation theorem, to solve the option pricing problem in a financial market, and to obtain the famous Black-Scholes formula, along with other results.

In particular, the book will provide the reader 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, and science.

Theory of Stochastic Differential Equations with Jumps and Applications will be a valuable reference for grad students and professionals in physics, chemistry, biology, engineering, finance and mathematics who are interested in problems such as the following:

mathematical description and analysis of stocks and shares;

option pricing, optimal consumption, arbitrage-free markets;

control theory and stochastic control theory and their applications;

non-linear filtering problems with jumps;

population control.

Keywords

Brownian motion Martingale Stochastic calculus differential equation linear optimization maximum principle point process

Bibliographic information

  • DOI https://doi.org/10.1007/b106901
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, Boston, MA
  • eBook Packages Engineering
  • Print ISBN 978-0-387-25083-0
  • Online ISBN 978-0-387-25175-2
  • Buy this book on publisher's site
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