Stochastic Financial Models / Edition 1

Stochastic Financial Models / Edition 1

by Douglas Kennedy
     
 

ISBN-10: 1420093452

ISBN-13: 9781420093452

Pub. Date: 01/15/2010

Publisher: Taylor & Francis

Filling the void between surveys of the field with relatively light mathematical content and books with a rigorous, formal approach to stochastic integration and probabilistic ideas, Stochastic Financial Models provides a sound introduction to mathematical finance. The author takes a classical applied mathematical approach, focusing on calculations rather

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Overview

Filling the void between surveys of the field with relatively light mathematical content and books with a rigorous, formal approach to stochastic integration and probabilistic ideas, Stochastic Financial Models provides a sound introduction to mathematical finance. The author takes a classical applied mathematical approach, focusing on calculations rather than seeking the greatest generality.

Developed from the esteemed author’s advanced undergraduate and graduate courses at the University of Cambridge, the text begins with the classical topics of utility and the mean-variance approach to portfolio choice. The remainder of the book deals with derivative pricing. The author fully explains the binomial model since it is central to understanding the pricing of derivatives by self-financing hedging portfolios. He then discusses the general discrete-time model, Brownian motion and the Black–Scholes model. The book concludes with a look at various interest-rate models. Concepts from measure-theoretic probability and solutions to the end-of-chapter exercises are provided in the appendices.

By exploring the important and exciting application area of mathematical finance, this text encourages students to learn more about probability, martingales and stochastic integration. It shows how mathematical concepts, such as the Black–Scholes and Gaussian random-field models, are used in financial situations.

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Product Details

ISBN-13:
9781420093452
Publisher:
Taylor & Francis
Publication date:
01/15/2010
Series:
Chapman and Hall/CRC Financial Mathematics Series
Pages:
264
Product dimensions:
6.10(w) x 9.30(h) x 0.80(d)

Table of Contents

Portfolio Choice
Introduction
Utility
Mean-variance analysis

The Binomial Model
One-period model
Multi-period model

A General Discrete-Time Model
One-period model
Multi-period model

Brownian Motion
Introduction
Hitting-time distributions
Girsanov’s theorem
Brownian motion as a limit
Stochastic calculus

The Black–Scholes Model
Introduction
The Black–Scholes formula
Hedging and the Black–Scholes equation
Path-dependent claims
Dividend-paying assets

Interest-Rate Models
Introduction
Survey of interest-rate models
Gaussian random-field model

Appendix A: Mathematical Preliminaries
Appendix B: Solutions to the Exercises

Further Reading

References

Index

Exercises appear at the end of each chapter.

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