Stochastic Calculus and Financial Applications

Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas.§From the reviews: "As the preface says, This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract . This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATHThe Wharton School course on which the book is based is designed for energetic students who have had some experience with probability and statistics, but who have not had advanced courses in stochastic processes. Even though the course assumes only a modest background, it moves quickly and - in the end - students can expect to have the tools that are deep enough and rich enough to be relied upon throughout their professional careers. §The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more demanding development of continuous time stochastic process, especially Brownian motion. The construction of Brownian motion is given in detail, and enough material on the subtle properties of Brownian paths is developed so that the student should sense of when intuition can be trusted and when it cannot. The course then takes up the It