隨機金融概要（簡體書）

本書主要目的有三，一、研究隨機分析必備內容以及不確定性下金融市場操縱模型中的估價；二、介紹主要概念、觀點以及隨機金融數學結果；三、講述結果在金融工程各種計算中的應用。
本書為金融數學和工程數學的讀者提供了概率統計的基本觀點和隨機分析市場風險的分析方法。書中不僅涵蓋了金融中能夠運用到的概率內容，也介紹了數學金融中的最新進展。既講述了金融理論又結合金融實踐，脈絡清晰流暢。每部分的講解從特殊到一般，從實例到結果。綜合性強，包含了數學金融、熵以及馬爾科夫理論。第二部分的學習需要對隨機微積分知識有相當的了解。目次：第一部分：事實，模型：主要概念、結構和工具，金融理論目標和問題以及金融工程；隨機模型，離散時間；隨機模型，連續時間；金融數據統計分析；第二部分：理論：隨機金融模型中的套利原理，離散時間；隨機金融模型中的價格理論，離散時間；隨機金融模型中的隨意理論，連續時間；隨機金融模型中的價格理論，連續時間。

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. Markowitzs 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