J. Michael Steele (auth.)0387950168, 9780387950167
This book is designed for students who want to develop professional skill in stochastic calculus and its application to problems in finance. The Wharton School course that forms the basis for this book is designed for energetic students who have had some experience with probability and statistics but have not had ad vanced courses in stochastic processes. Although the course assumes only a modest background, it moves quickly, and in the end, students can expect to have 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 de manding development of continuous-time stochastic processes, especially Brownian motion. The construction of Brownian motion is given in detail, and enough mate rial on the subtle nature of Brownian paths is developed for the student to evolve a good sense of when intuition can be trusted and when it cannot. The course then takes up the Ito integral in earnest. The development of stochastic integration aims to be careful and complete without being pedantic. |
Table of contents :
Front Matter….Pages i-ix
Random Walk and First Step Analysis….Pages 1-10
First Martingale Steps….Pages 11-28
Brownian Motion….Pages 29-42
Martingales: The Next Steps….Pages 43-60
Richness of Paths….Pages 61-78
Itô Integration….Pages 79-94
Localization and Itô’s Integral….Pages 95-109
Itô’s Formula….Pages 111-135
Stochastic Differential Equations….Pages 137-151
Arbitrage and SDEs….Pages 153-168
The Diffusion Equation….Pages 169-190
Representation Theorems….Pages 191-212
Girsanov Theory….Pages 213-231
Arbitrage and Martingales….Pages 233-261
The Feynman-Kac Connection….Pages 263-275
Back Matter….Pages 277-301 |
Reviews
There are no reviews yet.