Introduction to the mathematics of finance : from risk management to options pricing对财政的数学的介绍

作者： Steven Roman著

出 版 社：

出版时间： 2004-8-1字数：版次：页数： 354印刷时间： 2004/08/01开本： 16开印次：纸张： 胶版纸I S B N ： 9780387213644包装： 平装内容简介

The Mathematics of Finance has become a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options.

The mathematics is not watered down but is appropriate for the intended audience. No measure theory is used and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book also contains a chapter on options.

作者简介：

Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag. He has also written Modules in Mathematics, a series of 15 small books designed for the general college-level liberal arts student. Besides his books for O'Reilly, Dr. Roman has written two other computer books, both published by Springer-Verlag.

目录

Contents

Preface

Notation Key and Greek Alphabet

Introduction

Portfolio Risk Management

Option Pricing Models

Assumptions

Arbitrage

1 Probability I: An Introduction to Discrete Probability

1.1 Overview

1.2 Probability Spaces

1.3 Independence

1.4 Binomial Probabilities

1.5 Random Variables

1.6 Expectation

1.7 Variance and Standard Deviation

1.8 Covariance and Correlation; Best Linear Predictor

Exercises

2 Portfolio Management and the Capital Asset Pricing Model

2.1 Portfolios, Returns and Risk

2.2 Two-Asset Portfolios

2.3 Multi-Asset Portfolios

Exercises

3 Background on Options

3.1 Stock Options

3.2 The Purpose of Options

3.3 Profit and Payoff Curves

3.4 Selling Short

Exercises

4 An Aperitif on Arbitrage

4.1 Background on Forward Contracts

4.2 The Pricing of Forward Contracts

4.3 The Put-Call Option Parity Formula

4.4 Option Prices

Exercises

5 Probability II: More Discrete Probability

5.1 Conditional Probability

5.2 Partitions and Measurability

5.3 Algebras

5.4 Conditional Expectation

5.5 Stochastic Processes

5.6 Filtrations and Martingales

Exercises

6 Discrete-Time Pricing Models

6.1 Assumptions

6.2 Positive Random Variables

6.3 The Basic Model by Example

6.4 The Basic Model

6.5 Portfolios and Trading Strategies

6.6 The Pricing Problem: Alternatives and Replication

6.7 Arbitrage Trading Strategies

6.8 Admissible Arbitrage Trading Strategies

6.9 Characterizing Arbitrage

6.10 Computing Martingale Measures

Exercises

7 The Cox-Ross-Rubinstein Model

7.1 The Model

7.2 Martingale Measures in the CRR model

7.3 Pricing in the CRR Model

7.4 Another Look at the CRR Model via Random Walks

Exercises

8 Probability III: Continuous Probability

8.1 General Probability Spaces

8.2 Probability Measures on R

8.3 Distribution Functions

8.4 Density Functions

8.5 Types of Probability Measures on 1~

8.6 Random Variables

8.7 The Normal Distribution

8.8 Convergence in Distribution

8.9 The Central Limit Theorem

Exercises

9 The B lack-Scholes Option Pricing Formula

10 Optimal Stopping and American Options

Appendix A:Pricing Nonattainable Alternatives in an Incomplete Market

Appendix B:Convexity and the Separation Theorem

Selected Solutions

References

Index