A First Course in Stochastic Calculus

ISBN-13: 9781470464882

Louis-Pierre Arguin

Opis

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.

Spis treści

• Basic notions of probability
• Gaussian processes
• Properties of Brownian motion
• Martingales
• Ito calculus
• Multivariate Ito calculus
• Ito processes and stochastic differential equations
• The Markov property
• Change of probability
• Applications to mathematical finance
• Bibliography
• Index