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Stochastic Calculus and Differential Equations for Physics and Finance

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  • McCauley,Joseph L.

Abstract

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.

Suggested Citation

  • McCauley,Joseph L., 2013. "Stochastic Calculus and Differential Equations for Physics and Finance," Cambridge Books, Cambridge University Press, number 9780521763400, January.
    • Handle: RePEc:cup:cbooks:9780521763400
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    Cited by:

    1. Zapart, Christopher A., 2015. "Econophysics: A challenge to econometricians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 318-327.
    2. Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.
    3. Olkhov, Victor, 2016. "On Economic Space notion," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 372-381.
    4. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 330-344.

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