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

 Buch
Besorgungstitel | Lieferzeit:3-5 Tage I
ISBN-13:
9780387250830
Einband:
Buch
Erscheinungsdatum:
01.04.2005
Seiten:
434
Autor:
Rong Situ
Gewicht:
812 g
Format:
234x156x25 mm
Serie:
Mathematical and Analytical Te
Sprache:
Englisch
Beschreibung:

Derivation of Ito's formulas, Girsanov's theorems and martingale representation theorem for stochastic DEs with jumps
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.
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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