Stochastic Processes: From Physics to Finance

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Springer Science & Business Media, Jul 11, 2013 - Science - 280 pages
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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.
 

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Contents

A First Glimpse of Stochastic Processes
1
A Brief Survey of the Mathematics of Probability Theory
17
Diffusion Processes
62
Beyond the Central Limit Theorem Lévy Distributions
131
Modeling the Financial Market
163
Stable Distributions Revisited
236
Hyperspherical Polar Coordinates
243
The Weierstrass Random Walk Revisited
247
The Exponentially Truncated Lévy Flight
253
PutCall Parity
258
Geometric Brownian Motion
261
References
265
Index
273
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