Stochastic Processes - From Physics to Finance

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

List of contents

A First Glimpse of Stochastic Processes.- A Brief Survey of the Mathematics of Probability Theory.- Diffusion Processes.- Beyond the Central Limit Theorem: Lévy Distributions.- Modeling the Financial Market.- Stable Distributions Revisited.- Hyperspherical Polar Coordinates.- The Weierstrass Random Walk Revisited.- The Exponentially Truncated Lévy Flight.- Put-Call Parity.- Geometric Brownian Motion.

Report

From the book reviews:
"The authors, both physicists, have revised their successful book first published in 2000. ... the stochastic processes are presented clearly in mathematical language, e.g., with measure theoretical formalism, which makes the book readable for mathematicians. Its value for mathematicians, especially those who are already familiar with the basic ideas of mathematical finance, is in the many examples from physics, that provide a broad overview of the basic models and ideas of statistical physics." (Peter E. Kloeden, SIAM Review, Vol. 56 (4), December, 2014)

Product details

• Authors: Jorg Baschnagel, Jörg Baschnagel, Wolfgan Paul, Wolfgang Paul
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2015
• EAN: 9783319033785
• ISBN: 978-3-31-903378-5
• No. of pages: 280
• Dimensions: 155 mm x 235 mm x 15 mm
• Weight: 456 g
• Illustrations: XIII, 280 p. 43 illus.
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Social sciences, law, business > Business; B, Economic theory & philosophy, Economic Theory, Physics, Applications of Mathematics, Complex systems, Finance & accounting, Ecological science, the Biosphere, Physics and Astronomy, Mathematical physics, Economics, Mathematical, Quantitative Finance, Quantitative Economics, Mathematical Methods in Physics, Mathematical modelling, Mathematical Applications in the Physical Sciences, Economic Theory/Quantitative Economics/Mathematical Methods, Econophysics, Sociophysics, Data-driven Science, Modeling and Theory Building