A First Course in Stochastic Calculus is a complete guide for
advanced undergraduate students to take the next step in exploring
probability theory and for master's students in mathematical
finance who would like to build an intuitive and theoretical
understanding of stochastic processes. This book is also an
essential tool for finance professionals who wish to sharpen their
knowledge and intuition about stochastic calculus. Louis-Pierre
Arguin offers an exceptionally clear introduction to Brownian
motion and to random processes governed by the principles of
stochastic calculus. The beauty and power of the subject are made
accessible to readers with a basic knowledge of probability, linear
algebra, and multivariable calculus. This is achieved by
emphasizing numerical experiments using elementary Python coding to
build intuition and adhering to a rigorous geometric point of view
on the space of random variables. This unique approach is used to
elucidate the properties of Gaussian processes, martingales, and
diffusions. One of the book's highlights is a detailed and
self-contained account of stochastic calculus applications to
option pricing in finance.
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