随机金融概要
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作者： （俄罗斯）谢耶夫 著
出 版 社： 世界图书出版公司
出版时间： 2010-2-1字数：版次： 1页数： 834印刷时间： 2010-2-1开本： 24开印次： 1纸张： 胶版纸I S B N ： 9787510005367包装： 平装
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。第二部分的学习需要对随机微积分知识有相当的了解。目次：第一部分：事实，模型：主要概念、结构和工具，金融理论目标和问题以及金融工程；随机模型，离散时间；随机模型，连续时间；金融数据统计分析；第二部分：理论：随机金融模型中的套利原理，离散时间；随机金融模型中的价格理论，离散时间；随机金融模型中的随意理论，连续时间；随机金融模型中的价格理论，连续时间。
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
1. Necessary probabilistic concepts and several models of the dynamics of market prices
1a. Uncertainty and irregu1arity in the behavior of prices. Their description and representation in probabilistic terms
1b. Doob decomposition. Canonical representations
1c. Local martingales. Martingale transformations. Generalized martingales
1d. Gaussian and conditionally Gaussian models
1e. Binomial model of price evolution
1f. Models with discrete intervention of chance
2. Linear stochastic models
2a. Moving average model MA(q)
12b. Autoregressive model AR(p)
12c. Autoregressive and moving average model ARMA(p, q)and integrated model ARIMA(p, d, q)
12d. Prediction in linear models
3. Nonlinear stochastic conditionally Gaussian models
3a. ARCH and GARCH models
3b. EGARCH, TGARCH, HARCH, and other models
3c. Stochastic vo1atility models
4. Supplement: dynamical chaos models
4a. Nonlinear chaotic models
4b. Distinguishing between 'chaotic' and 'stochastic' sequences
Chapter Ⅲ Stochastic Models. Continuous Time
Chapter Ⅳ Statistical Analysis of Financial Data
Chapter V. Theory of Arbitrage in Stochastic Financial Models Discrete Time
ChapterⅥ Theory of Pricing in Stochastic Financial Models. Discrete Time
Chapter Ⅶ Theory of Arbitrage in Stochastic Financial
Chapter Ⅷ Theory of Pricing in Stochastic Financial
Bibliography
Index
Index of symbols
