Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis, for example: the It calculus, stochastic control, differential equations, and martingales. The authors give rigorous treatments of these topics, while always keeping the applications in...