This book of problems has been designed to accompany an undergraduate course in probability. It will also be useful for students with interest in probability who wish to study on their own. The only prerequisite is basic algebra and calculus. This includes some elementary experience in set theory, sequences and series, functions of one variable, and their derivatives. Familiarity with integrals would be a bonus. A brief survey of terminology and notation in set theory and calculus is provided. Each chapter is divided into three parts: Problems, Hints, and Solutions. To make the book...

The erratic motion of pollen grains and other tiny particles suspended in liquid is known as Brownian motion, after its discoverer, Robert Brown, a botanist who worked in 1828, in London. He turned over the problem of why this motion occurred to physicists who were investigating kinetic theory and thermodynamics; at a time when the existence of molecules had yet to be established. In 1900, Henri Poincare lectured on this topic to the 1900 International Congress of Physicists, in Paris Wic95]. At this time, Louis Bachelier, a thesis student of Poincare, made a monumental breakthrough with his...

Driven by concrete computational problems in quantitative finance, this book provides aspiring quant developers with the numerical techniques and programming skills they need. The authors start from scratch, so the reader does not need any previous experience of C++. Beginning with straightforward option pricing on binomial trees, the book gradually progresses towards more advanced topics, including nonlinear solvers, Monte Carlo techniques for path-dependent derivative securities, finite difference methods for partial differential equations, and American option pricing by solving a linear...