This comprehensive course on financial mathematics is aimed at beginning graduate students in any field with a good quantitative background, and is appropriate for advanced undergraduates in mathematics and statistics. It is also invaluable as a reference for practitioners in financial engineering. Via an accessible presentation of the theory of probability and stochastic processes needed to construct and employ most models commonly used in investment finance, including binomial trees, Brownian motion, martingales, Markov processes, and Levy processes, the book covers no-arbitrage option...