Stochastic Calculus and Financial Applications (Hardback)

Condition

GOOD: This book is in excellent condition, but because a previous owner's name is written on the front end page, it can only be graded as good. No other pages have writing on them. The book was printed on acid-free paper.

Product Details

This book is Volume 45 in theStochastic Modelling and Applied Probability series from Springer.

From the back cover: "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 on 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 evolve a good sense of when intuition can be trusted and when it cannot. The course then takes up the Itö integral and aims to provide a development that is honest and complete without being pedantic.

"With the Itö integral in hand, the course focuses more on models. Stochastic processes of importance in finance and economics are developed in concert with the tools of stochastic calculus that are needed in order to solve problems of practical importance. The financial notion of replication is developed, and the Black-Scholes PDE is derived by three different methods. The course then introduces enough of the theory of the diffusion equation to be able to solve the Black-Scholes PDE and prove the uniqueness of the solution. The foundations for the martingale theory of arbitrage pricing are then prefaced by a well-motivated development of the martingale representation theorems and Girsanov theory. Arbitrage pricing is then revisited and the notions of attainability and completeness are developed in order to give a clear view of the fundamental formula for the pricing of contingent claims."

BRIEF CONTENTS