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  22. Heavy Traffic Analysis of Controlled Queueing and Communication Networks
  23. Stochastic Portfolio Theory
  24. Linear Geometry
  25. Applied Probability & Queues 2ND Edition
  26. Monte Carlo Methods in Financial Engineering
  27. Discrete-time Markov Chains
  28. The Arithmetic of Elliptic Curves
  29. Imperfect Bifurcation in Structures and Materials
  30. Front Tracking for Hyberbolic Conservation Laws
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Applications of Mathematics #45: Stochastic Calculus and Financial Applications

by J. Michael Steele

Applications of Mathematics #45: Stochastic Calculus and Financial Applications Cover

Synopses & Reviews

Publisher Comments:

This book is designed for students who want to develop professional skills in stochastic calculus and its application to problems in finance. 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 Itô integral and aims to provide a development that is honest and complete without being pedantic.With the Itô 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.

Synopsis:

This text aims to develop professional skills in stochastic calculus and its application to problems in finance. The Wharton School course on which the book is based is designed for those with some experience with probability and statistics, but not in stochastic processes.

Synopsis:

Designed as an introduction to stochastic calculus and its application to mathematical finance, Steele gives the reader tools that are deep and rich enough to be used throughout their professional careers, with a focus on mathematical finance and economics.
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Table of Contents

Random Walk and First Step Analysis.- First Martingale Steps.- Brownian Motion.- Martingale: The Next Steps.- Richness of Paths.- Itô Integration.- Localization and Itô's Integral.- Itô's Formula.- Stochastic Differential Equations.- Arbitrage and SDEs.- The Diffusion Equation.- Representation Theorem.- Girsanov Theory.- Arbitrage and Martingales.- The Feynman-Kac Connection.- Appendix I. Mathematical Tools.- Appendix II. Comments and Credits.- Bibliography.- Index.

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What Our Readers Are Saying

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Average customer rating based on 1 comment:
nmsmisra, December 22, 2006 (view all comments by nmsmisra)
Its one of very good book that give complete illustration of use of Stochastic Calculus to finance , beginning from very first chapter (binomial no-arbitrage pricing model) and second chapter(probability theory on coin and toss space) that give an overview of the pricing model and probability respectively , it maintain its nice flow and go deeper to the subject , its third (state prices) is really remarkable and fourth chapter give quite a lot about the American derivative security fifth and sixth chapter go in depth of the subject and complete the aim of this book.
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Product Details

ISBN:
9780387950167
Author:
Steele, J. M.
Publisher:
Springer
Author:
Steele, J. M.
Location:
New York
Subject:
General
Subject:
Probability
Subject:
Business mathematics
Subject:
Stochastic analysis
Subject:
Probability & Statistics - General
Copyright:
2003
Edition Number:
1
Edition Description:
2001. Corr. 3rd
Series:
Applications of Mathematics
Series Volume:
[29]45
Publication Date:
June 2003
Binding:
Hardcover
Language:
English
Illustrations:
Y
Pages:
300
Dimensions:
9.46x6.38x.77 in. 1.23 lbs.
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