@inbook{642615da1a2f4b96873260bfbdf6c103,
title = "The Stochastic Differential Equation",
abstract = "To develop the hedging argument of Black and Scholes, this chapter introduces stochastic differential equations to model the evolution of the price path itself and the statistical properties of small price changes over small changes in time. We then consider the stochastic differential equations for the Wiener process, Ornstein–Uhlenbeck process and Poisson process and examine the autocovariance behaviour of the Wiener process. Furthermore we introduce stochastic integrals to define the stochastic differential equations.",
keywords = "Planck Equation, Price Change, Sample Path, Stochastic Differential Equation, Wiener Process",
author = "Carl Chiarella and He, {Xue Zhong} and Nikitopoulos, {Christina Sklibosios}",
note = "Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",
year = "2015",
doi = "10.1007/978-3-662-45906-5_4",
language = "English",
series = "Dynamic Modeling and Econometrics in Economics and Finance",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "55--91",
booktitle = "Dynamic Modeling and Econometrics in Economics and Finance",
}