Description
Book SynopsisA 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.
Trade ReviewLouis-Pierre Arguin's masterly introduction to stochastic calculus seduces the reader with its quietly conversational style; even rigorous proofs seem natural and easy. Full of insights and intuition, reinforced with many examples, numerical projects, and exercises, this book by a prize-winning mathematician and great teacher fully lives up to the author's reputation. I give it my strongest possible recommendation."" —Jim Gatheral, Baruch College
""I happen to be of a different persuasion, about how stochastic processes should be taught to undergraduate and MA students. But I have long been thinking to go against my own grain at some point and try to teach the subject at this level—together with its applications to finance—in one semester. Louis-Pierre Arguin's excellent and artfully designed text will give me the ideal vehicle to do so."" —Ioannis Karatzas, Columbia University, New York
Table of Contents
- 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
