Graduate Studies in Mathematics 2001; 253 pp; hardcover Volume: 31 ISBN10: 0821821237 ISBN13: 9780821821237 List Price: US$45 Member Price: US$36 Order Code: GSM/31
 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: the Itô calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of purely mathematical topics are treated in extended "excursions" from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a selfcontained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes an applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuoustime finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential. Readership Graduate level and research mathematicians, physicists, financial analysts, and actuarians interested in mathematical finance. Reviews "Especially useful for students seeking a lively introduction to Itô calculus."  Short Book Reviews, International Statistical Institute Table of Contents  The meanvariance approach in a oneperiod model
 The continuoustime market model
 Option pricing
 Pricing of exotic options and numerical algorithms
 Optimal portfolios
 Bibliography
 Index
