本书主要目的有三，一、研究随机分析必备内容以及不确定性下金融市场操纵模型中的估价；二、介绍主要概念、观点以及随机金融数学结果；三、讲述结果在金融工程各种计算中的应用。

本书为金融数学和工程数学的读者提供了概率统计的基本观点和随机分析市场风险的分析方法。书中不仅涵盖了金融中能够运用到的概率内容，也介绍了数学金融中的最新进展。既讲述了金融理论又结合金融实践，脉络清晰流畅。每部分的讲解从特殊到一般，从实例到结果。综合性强，包含了数学金融、熵以及马尔科夫理论。

Foreword

Part 1.Facts.Models

Chapter Ⅰ Main Concepts, Structures, and Instruments.Aims and Problems of Financial Theory and Financial Engineering

1.Financial structures and instruments

 1a.Key objects and structures

 1b.Financial markets

 1c.Market of derivatives.Financial instruments

2.Financial markets under uncertainty.C1assical theories of the dynamics of financial indexes, their critics and revision.Neoc1assical theories

 2a.Random walk conjecture and concept of efficient market

 2b.Investment portfolio.Markowitz's diversification

 2c.CAPM: Capital Asset Pricing Model

 2d.APT: Arbitrage Pricing Theory

 2e.Analysis, interpretation, and revision of the c1assical concepts of efficient market.I

 2f.Analysis, interpretation, and revision of the c1assical concepts of efficient market.Ⅱ

3.Aims and problems of financial theory, engineering, and actuarial calcu1ations

 3a.Role of financial theory and financial engineering.Financial risks

 3b.Insurance: a social mechanism of compensation for financial losses

 3c.A c1assical example of actuarial calcu1ations: the Lundberg-Cram6r theorem

Chapter Ⅱ Stochastic Models.Discrete Time

Chapter Ⅲ Stochastic Models. Continuous Time

Chapter Ⅳ Statistical Analysis of Financial Data

Part 2.Theory

Chapter Ⅴ. Theory of Arbitrage in Stochastic Financial Models Discrete Time

Chapter Ⅵ Theory of Pricing in Stochastic Financial Models. Discrete Time

Chapter Ⅶ Theory of Arbitrage in Stochastic Financial Models.Continuous Time

Chapter Ⅷ Theory of Pricing in Stochastic Financial Models.Continuous Time

Bibliography

Index

Index of symbols