Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering / Edition 1

by Rong SITU

Overview

Shastic 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 shastic 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.

Product Details

ISBN-13:	9780387250830
Publisher:	Springer US
Publication date:	04/20/2005
Series:	Mathematical and Analytical Techniques with Applications to Engineering
Edition description:	2005
Pages:	434
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Shastic Differential Equations with Jumps in Rd.- Martingale Theory and the Shastic Integral for Point Processes.- Brownian Motion, Shastic Integral and Ito's Formula.- Shastic Differential Equations.- Some Useful Tools in Shastic Differential Equations.- Shastic Differential Equations with Non-Lipschitzian Coefficients.- Applications.- How to Use the Shastic Calculus to Solve SDE.- Linear and Non-linear Filtering.- Option Pricing in a Financial Market and BSDE.- Optimal Consumption by H-J-B Equation and Lagrange Method.- Comparison Theorem and Shastic Pathwise Control.- Shastic Population Control and Reflecting SDE.- Maximum Principle for Shastic Systems with Jumps.