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.
Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.
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.
'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
'Joe McCauley's book fills a gap in the current literature by
providing a clear and readable introduction to stochastic calculus
and stochastic differential equations for physicists. His book is
written in a style that will not deter physicists and other applied
scientists from learning these important topics.' Enrico Scalas,
University of East Piedmont
'Joe McCauley continues the tradition he has established for
clarity of exposition, at the frontiers of research, in fields
whose practitioners are in sore need of it. This book is an
outstanding contribution to the mathematical needs of able
financial theorists who are also interested in underpinning
empirical work in sound mathematical theory. I do not think there
is any other book that undertakes the difficult tasks McCauley has
undertaken in this impeccably well crafted, yet deep and rigorous,
book.' K. Vela Velupillai, The New School for Social Research
'This book represents a rare and successful effort to provide a
unified treatment of continuous time stochastic processes derived
from both finance and physics. It constitutes an effective guide
for physicists trying to understand the models of modern finance
and for students of mathematical finance looking for methods
neglected by the traditional books on the subject. The intuitive
presentation of models in terms of physical and financial phenomena
and the constant attention to their practical applicability make
this book extremely useful also for those already knowledgeable
about the subject.' Giulio Bottazzi, Scuola Superiore Sant'Anna
'… [this] book contains a wealth of useful information and most
importantly helpful details. … [it] is further complemented by
adding a discussion of historical developments of statistical
physics and financial theory, taking into account their
similarities and differences. … Stochastic Calculus and
Differential Equations for Physics and Finance is a recommended
title that both the physicist and the mathematician will find of
interest.' Jesus Rogel-Salazar, Contemporary Physics
'The book gives a good introduction to stochastic calculus and is a
helpful supplement to other well-known books on this topic. It may
be recommended to graduate students in finance, stochastic analysis
and physics, as well as practitioners of this field.' Oliver Janke,
Zentralblatt MATH
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