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Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering de Rong SITU

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

Autor Rong SITU
en Limba Engleză Paperback – 8 dec 2010
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.
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Specificații

ISBN-13: 9781441937711
ISBN-10: 1441937714
Pagini: 456
Ilustrații: XX, 434 p.
Dimensiuni: 155 x 235 x 24 mm
Greutate: 0.64 kg
Ediția:Softcover reprint of hardcover 1st ed. 2005
Editura: Springer Us
Colecția Springer
Seria Mathematical and Analytical Techniques with Applications to Engineering

Locul publicării:New York, NY, United States

Public țintă

Professional/practitioner

Cuprins

Stochastic Differential Equations with Jumps in Rd.- Martingale Theory and the Stochastic Integral for Point Processes.- Brownian Motion, Stochastic Integral and Ito's Formula.- Stochastic Differential Equations.- Some Useful Tools in Stochastic Differential Equations.- Stochastic Differential Equations with Non-Lipschitzian Coefficients.- Applications.- How to Use the Stochastic 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 Stochastic Pathwise Control.- Stochastic Population Control and Reflecting SDE.- Maximum Principle for Stochastic Systems with Jumps.

Textul de pe ultima copertă

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.

Caracteristici

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