Joseph L. McCauley

Stochastic Calculus and Differential Equations for Physics and Finance (eBook, PDF)

• Format: PDF

Produktbeschreibung

Stochastic calculus provides a powerful description of a specific class of stochastic processes in physics and finance. However, many econophysicists struggle to understand it. This book presents the subject simply and systematically, giving graduate students and practitioners a better understanding and enabling them to apply the methods in practice. The book develops Ito calculus and Fokker-Planck equations as parallel approaches to stochastic processes, using those methods in a unified way. The focus is on nonstationary processes, and statistical ensembles are emphasized in time series analysis. Stochastic calculus is developed using general martingales. Scaling and fat tails are presented via diffusive models. Fractional Brownian motion is thoroughly analyzed and contrasted with Ito processes. The Chapman-Kolmogorov and Fokker-Planck equations are shown in theory and by example to be more general than a Markov process. The book also presents new ideas in financial economics and a critical survey of econometrics.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 21. Februar 2013
• Englisch
• ISBN-13: 9781107330627
• Artikelnr.: 52849352

Autorenporträt

Joseph L. McCauley is Professor of Physics at the University of Houston. During his career he has contributed to several fields, including statistical physics, superfluids, nonlinear dynamics, cosmology, econophysics, economics and finance theory.

Inhaltsangabe

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Rezensionen

'This new book by Joe McCauley is a most welcome and innovative contribution to the important field of mathematical finance theory. It presents a unified, rigorous and comprehensive framework of the dynamics of stochastic calculus that should underpin the mathematics of finance. The book's welcome focus on nonstationary processes and statistical ensembles in time series analysis, developing, inter alia, the Ito calculus and the Fokker-Planck equations as parallel approaches to stochastic processes, will make this the classic and indispensable textbook for any serious graduate courses in applied finance theory - not just for economists, but also for physicists interested in studying the world of finance.' Stefano Zambelli, Algorithmic Social Sciences Research Unit (ASSRU), University of Trento