Stochastic Processes

1. Front Matter

   Pages I-XIII

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2. A First Glimpse of Stochastic Processes

   • Wolfgang Paul, Jörg Baschnagel

   Pages 1-16

3. A Brief Survey of the Mathematics of Probability Theory

   • Wolfgang Paul, Jörg Baschnagel

   Pages 17-61

4. Diffusion Processes

   • Wolfgang Paul, Jörg Baschnagel

   Pages 63-129

5. Beyond the Central Limit Theorem: Lévy Distributions

   • Wolfgang Paul, Jörg Baschnagel

   Pages 131-162

6. Modeling the Financial Market

   • Wolfgang Paul, Jörg Baschnagel

   Pages 163-235

7. Back Matter

   Pages 237-280

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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.

• Brownian Motion
• Econophysics of Financial Crashes
• Exponentially Truncated Lévy Flight
• Levy Distributions
• Modeling the Financial Market
• Put–Call Parity
• Stochastic Mechanics
• Stochastic Processes
• Weierstrass Random Walk
• data-driven science, modeling and theory building
• quantitative finance

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)

• Halle-Wittenberg, Martin-Luther-Universität, Halle (Saale), Germany

  Wolfgang Paul

• Institut Charles Sadron, Université de Strasbourg, Strasbourg Cedex 2, France

  Jörg Baschnagel

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