Theory of Stochastic Differential Equations with Jumps and Applications
Mathematical and Analytical Techniques with Applications to Engineering
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Beschreibung
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.
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.
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
Autor*in
Rong SITU
Themen in »Theory of Stochastic Differential Equations with Jumps and Applications«
Brownian motion Martingale Stochastic calculus differential equation linear optimization maximum principle point process