Stochastic Calculus and Financial Applications

ISBN-10: 0387950168

ISBN-13: 9780387950167

Edition: 2001

Authors: J. M. Steele

List price: $99.00
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Description:

The 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 integral and aims to provide a development that is honest and complete without being pedantic. With the It 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 equationto be able to solve the Black-Scholes PDE and prove the uniqueness of thesolution.
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Book details

List price: $99.00
Copyright year: 2001
Publisher: Springer
Publication date: 6/27/2003
Binding: Hardcover
Pages: 302
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 1.232
Language: English

Random Walk and First Step Analysis
First Martingale Steps
Brownian Motion
Martingale--Next Steps
Richness of Paths
It+' Integration
Localization and It+'s Integral
It+'s Formula
Stochastic Differential Equations
Arbitrage and SDE's
The Diffusion Equation
Representation Theorems
Girsanov Theory
Arbitrage and Martingales
The Feynman-Kac Connection
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