罗斯所著的《数理金融初步(英文版第3版)》清晰简洁地阐述了数理金融学的基本问题，主要包括套利、Black-Scholes期权定价公式以及效用函数、最优资产组合原理、资本资产定价模型等知识，并将书中所讨论的问题的经济背景、解决这些问题的数学方法和基本思想系统地展示给读者。

本书内容选择得当、结构安排合理，既适合作为高等院校学生（包括财经类专业及应用数学专业）的教材，同时也适合从事金融工作的人员阅读。

罗斯所著的《数理金融初步(英文版第3版)》基于期权定价全面介绍数理金融学的基本问题，数理推导严密，内容深入浅出，适合受过有限数学训练的专业交易员和高等院校相关专业本科生阅读。本书清晰简洁地阐述了套利、Black-Scholes期权定价公式、效用函数、最优投资组合选择、资本资产定价模型等知识。

《数理金融初步(英文版第3版)》在第2版的基础上新增了布朗运动与几何布朗运动、随机序关系、随机动态规划等内容，并且扩展了每一章的习题和参考文献。

Introduction and Preface

1 Probability

 1.1 Probabilities and Events

 1.2 Conditional Probability

 1.3 Random Variables and Expected Values

 1.4 Covariance and Correlation

 1.5 Conditional Expectation

 1.6 Exercises

2 Normal Random Variables

 2.1 Continuous Random Variables

 2.2 Normal Random Variables

 2.3 Properties of Normal Random Variables

 2.4 The Central Limit Theorem

 2.5 Exercises

3 Brownian Motion and Geometric Brownian Motion

 3.1 Brownian Motion

 3.2 Brownian Motion as a Limit of Simpler Models

 3.3 Geometric Brownian Motion

3.3.1 Geometric Brownian Motion as a Limit of Simpler Models

 3.4 *The Maximum Variable

 3.5 The Cameron-Martin Theorem

 3.6 Exercises

4 Interest Rates and Present Value Analysis

 4.1 Interest Rates

 4.2 Present Value Analysis

 4.3 Rate of Return

 4.4 Continuously Varying Interest Rates

 4.5 Exercises

5 Pricing Contracts via Arbitrage

 5.1 An Example in Options Pricing

 5.2 Other Examples of Pricing via Arbitrage

 5.3 Exercises

6 The Arbitrage Theorem

 6.1 The Arbitrage Theorem

 6.2 The Multiperiod Binomial Model

 6.3 Proof of the Arbitrage Theorem

 6.4 Exercises

7 The Black-Scboles Formula

 7.1 Introduction

 7.2 The Black-Scholes Formula

 7.3 Properties of the Black-Scholes Option Cost

 7.4 The Delta Hedging Arbitrage Strategy

 7.5 Some Derivations

7.5.1 The Black-Scholes Formula

7.5.2 The Partial Derivatives

 7.6 European Put Options

 7.7 Exercises

8 Additional Results on Options

 8.1 Introduction

 8.2 Call Options on Dividend-Paying Securities

8.2.1 The Dividend for Each Share of the Security

 Is Paid Continuously in Time at a Rate Equal

 to a Fixed Fraction f of the Price of the

 Security

8.2.2 For Each Share Owned, a Single Payment of

 fS(td) IS Made at Time td

8.2.3 For Each Share Owned, a Fixed Amount D Is

 to Be Paid at Time td

 8.3 Pricing American Put Options

 8.4 Adding Jumps to Geometric Brownian Motion

8.4.1 When the Jump Distribution Is Lognormal

8.4.2 When the Jump Distribution Is General

 8.5 Estimating the Volatility Parameter

8.5.1 Estimating a Population Mean and Variance

8.5.2 The Standard Estimator of Volatility

8.5.3 Using Opening and Closing Data

8.5.4 Using Opening, Closing, and High-Low Data

 8.6 Some Comments

8.6.1 When the Option Cost Differs from the Black-Scholes Formula

8.6.2 When the Interest Rate Changes

8.6.3 Final Comments

 8.7 Appendix

 8.8 Exercises

9 Valuing by Expected Utility

 9.1 Limitations of Arbitrage Pricing

 9.2 Valuing Investments by Expected Utility

 9.3 The Portfolio Selection Problem

9.3.1 Estimating Covariances

 9.4 Value at Risk and Conditional Value at Risk

 9.5 The Capital Assets Pricing Model

 9.6 Rates of Return: Single-Period and Geometric

Brownian Motion

 9.7 Exercises

10 Stochastic Order Relations

 10.1 First-Order Stochastic Dominance

 10.2 Using Coupling to Show Stochastic Dominance

 10.3 Likelihood Ratio Ordering

 10.4 A Single-Period Investment Problem

 10.5 Second-Order Dominance

10.5.1 Normal Random Variables

10.5.2 More on Second-Order Dominance

 10.6 Exercises

11 Optimization Models

 11.1 Introduction

 11.2 A Deterministic Optimization Model

11.2.1 A General Solution Technique Based on

  Dynamic Programming

11.2.2 A Solution Technique for Concave

  Return Functions

11.2.3 The Knapsack Problem

 11.3 Probabilistic Optimization Problems

11.3.1 A Gambling Model with Unknown Win Probabilities

11.3.2 An Investment Allocation Model

 11.4 Exercises

12 Stochastic Dynamic Programming

 12.1 The Stochastic Dynamic Programming Problem

 12.2 Infinite Time Models

 12.3 Optimal Stopping Problems

 12.4 Exercises

13 Exotic Options

 13.1 Introduction

 13.2 Barrier Options

 13.3 Asian and Lookback Options

 13.4 Monte Carlo Simulation

 13.5 Pricing Exotic Options by Simulation

 13.6 More Efficient Simulation Estimators

13.6.1 Control and Antithetic Variables in the

  Simulation of Asian and Lookback

  Option Valuations

13.6.2 Combining Conditional Expectation and

  Importance Sampling in the Simulation of

  Barrier Option Valuations

  13.7 Options with Nonlinear Payoffs

  13.8 Pricing Approximations via Multiperiod Binomial Models

  13.9 Continuous Time Approximations of Barrier and Lookback Options

  13.10 Exercises

14 Beyond Geometric Brownian Motion Models

  14.1 Introduction

  14.2 Crude Oil Data

  14.3 Models for the Crude Oil Data

  14.4 Final Comments

15 Autoregressive Models and Mean Reversion

  15.1 The Autoregressive Model

  15.2 Valuing Options by Their Expected Return

  15.3 Mean Reversion

  15.4 Exercises

Index