Product Description

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.

Product Details

• Amazon Sales Rank: #119554 in Books
• Published on: 2004-09-28
• Original language: English
• Number of items: 1
• Binding: Paperback
• 470 pages

Customer Reviews

a must reading for quants working in economics and finance
Before young talents try to prove themselves in this area they must know what is known... Karatzas and Shreve offered an intensive, rigorous and covering text on stochastic processes. Especially needed for quants working in the hottest applications, economics and finance, where demand is rapidly growing, but the qualifications should essentially be based on "Brownian Motion..." Warning: the book is for advanced readers; be ready for some overwhelming notations. Harder-than-usual efforts are required, by they will ultimately pay off.