随机金融概要（英文版）
目 录内容简介
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
1. Non-Gaussian models of distributions and processes.
1a. Stable and infinitely divisible distributions
1b. Levy processes
1c. Stable processes
1d. Hyperbolic distributions and processes
2. Models with self-simi1arity. Fractality
2a. Hursts statistical phenomenon of self-simi1arity
2b. A digression on fractal geometry
2c. Statistical self-simi1arity. Fractal Brownian motion
2d. Fractional Gaussian noise： a process with strong aftereffect
3. Models based on a Brownian motion
3a. Brownian motion and its role of a basic process
3b. Brownian motion： a compendium of c1assical results
3c. Stochastic integration with respect to a Brownian motion
3d. It5 processes and ItSs formu1a
3e. Stochastic differential equations
3f. Forward and backward Kolmogorovs equations. Probabilistic representation of solutions
4. Diffusion models of the evolution of interest rates， stock and bond prices
4a. Stochastic interest rates
4b. Standard diffusion model of stock prices (geometric Brownian motion) and its generalizations
4c. Diffusion models of the term structure of prices in a family of bonds
5. Semimartingale models
5a. Semimartingales and stochastic integrals
5b. Doob-Meyer decomposition. Compensators. Quadratic variation
5c. itSs formu1a for semimartingales. Generalizations
Chapter Ⅳ Statistical Analysis of Financial Data
1. Empirical data. Probabilistic and statistical models of their description. Statistics of ticks.
1a. Structural changes in financial data gathering and analysis
1b. Geography-re1ated features of the statistical data on exchange rates
1c. Description of financial indexes as stochastic processes with discrete intervention of chance
1d. On the statistics of ticks
2. Statistics of one-dimensional distributions
2a.Statistical data discretizing
2b.One-dimensional distributions of the logarithms of re1ative price changes. Deviation from the Gaussian property
and leptokurtosis of empirical densities
2c.One-dimensional distributions of the logarithms of relative price changes. Heavy tails and their statistics
2d.One-dimensional distributions of the logarithms of re1ative price changes. Structure of the central parts of distributions
3. Statistics of vo1atility， corre1ation dependence and aftereffect in prices
3a. Vo1atility. Definition and examples
3b. Periodicity and fractal structure of vo1atility in exchange rates
3c. Corre1ation properties
3d. Devo1atization. Operational time
3e.Cluster phenomenon and aftereffect in prices
4. Statistical R/S-analysis.
4a. Sources and methods of R/S-analysis
4b. R/S-analysis of some financial time series
Part 2. Theory
Chapter V. Theory of Arbitrage in Stochastic Financial Models Discrete Time
1. Investment portfolio on a (B， S)-market
1a. Strategies satisfying ba1ance conditions
1b. Notion of hedging. Upper and lower prices Complete and incomplete markets
1c. Upper and lower prices in a single-step model
1d. CRR-model： an example of a complete market
2. Arbitral：e-free market
2a. Arbitrage and absence of arbitrage
2b. Martingale criterion of the absence of arbitrage First fundamental theorem
2c. Martingale criterion of the absence of arbitrage Proof of sufficiency
2d. Martingale criterion of the absence of arbitrage Proof of necessity (by means of the Esscher conditional transformation)
2e. Extended version of the First fundamental theorem
3. Construction of martingale measures
by means of an absolutely continuous change ot measure
3a. Main definitions. Density process
3b. Discrete version of Girsanovs theorem. Conditionally Gaussian case
3c. Martingale property of the prices in the case of a conditionally Gaussian and logarithmically conditionally Gaussian distributions
3d. Discrete version of Girsanovs theorem. General case
3e. Integer-valued random measures and their compensators.Transformation of compensators under absolutely continuous changes of measures. Stochastic integrals.
3f. Predictable criteria of arbitrage-free (B， S)-markets
……
ChapterⅥ Theory of Pricing in Stochastic Financial Models. Discrete Time
1. European hedge pricing on arbitrage-free markets
2. American hedge pricing on arbitrage-free markets
3. Scheme of series of large arbitrage-free markets and asymptotic arbitrage
4. European options on a binomial (B， S)-market
5. American options on a binomial (B， S)-market
Chapter Ⅶ Theory of Arbitrage in Stochastic Financial Models.Continuous Time
1. Investment portfolio in semimartingale models
2. Semimartingale models without opportunities for arbitrage.Completeness
3. Semimartingale and martingale measures
4. Arbitrage， completeness， and hedge pricing in diffusion models of stock
5. Arbitrage， completeness， and hedge pricing in diffusion models of bonds
Chapter Ⅷ Theory of Pricing in Stochastic Financial Models.Continuous Time
1. European options in diffusion (B， S)-stockmarkets
2. American options in diffusion (B， S)-stoekmarkets.Case of an infinite time horizon
3. American options in diffusion (B， S)-stockmarkets.Finite time horizons
4. European and American options in a diffusion(B， P)-bondmarket
Bibliography
Index
Index of symbols
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
1. Non-Gaussian models of distributions and processes.
1a. Stable and infinitely divisible distributions
1b. Levy processes
1c. Stable processes
1d. Hyperbolic distributions and processes
2. Models with self-simi1arity. Fractality
2a. Hursts statistical phenomenon of self-simi1arity
2b. A digression on fractal geometry
2c. Statistical self-simi1arity. Fractal Brownian motion
2d. Fractional Gaussian noise： a process with strong aftereffect
3. Models based on a Brownian motion
3a. Brownian motion and its role of a basic process
3b. Brownian motion： a compendium of c1assical results
3c. Stochastic integration with respect to a Brownian motion
3d. It5 processes and ItSs formu1a
3e. Stochastic differential equations
3f. Forward and backward Kolmogorovs equations. Probabilistic representation of solutions
4. Diffusion models of the evolution of interest rates， stock and bond prices
4a. Stochastic interest rates
4b. Standard diffusion model of stock prices (geometric Brownian motion) and its generalizations
4c. Diffusion models of the term structure of prices in a family of bonds
5. Semimartingale models
5a. Semimartingales and stochastic integrals
5b. Doob-Meyer decomposition. Compensators. Quadratic variation
5c. itSs formu1a for semimartingales. Generalizations
Chapter Ⅳ Statistical Analysis of Financial Data
1. Empirical data. Probabilistic and statistical models of their description. Statistics of ticks.
1a. Structural changes in financial data gathering and analysis
1b. Geography-re1ated features of the statistical data on exchange rates
1c. Description of financial indexes as stochastic processes with discrete intervention of chance
1d. On the statistics of ticks
2. Statistics of one-dimensional distributions
2a.Statistical data discretizing
2b.One-dimensional distributions of the logarithms of re1ative price changes. Deviation from the Gaussian property
and leptokurtosis of empirical densities
2c.One-dimensional distributions of the logarithms of relative price changes. Heavy tails and their statistics
2d.One-dimensional distributions of the logarithms of re1ative price changes. Structure of the central parts of distributions
3. Statistics of vo1atility， corre1ation dependence and aftereffect in prices
3a. Vo1atility. Definition and examples
3b. Periodicity and fractal structure of vo1atility in exchange rates
3c. Corre1ation properties
3d. Devo1atization. Operational time
3e.Cluster phenomenon and aftereffect in prices
4. Statistical R/S-analysis.
4a. Sources and methods of R/S-analysis
4b. R/S-analysis of some financial time series
Part 2. Theory
Chapter V. Theory of Arbitrage in Stochastic Financial Models Discrete Time
1. Investment portfolio on a (B， S)-market
1a. Strategies satisfying ba1ance conditions
1b. Notion of hedging. Upper and lower prices Complete and incomplete markets
1c. Upper and lower prices in a single-step model
1d. CRR-model： an example of a complete market
2. Arbitral：e-free market
2a. Arbitrage and absence of arbitrage
2b. Martingale criterion of the absence of arbitrage First fundamental theorem
2c. Martingale criterion of the absence of arbitrage Proof of sufficiency
2d. Martingale criterion of the absence of arbitrage Proof of necessity (by means of the Esscher conditional transformation)
2e. Extended version of the First fundamental theorem
3. Construction of martingale measures
by means of an absolutely continuous change ot measure
3a. Main definitions. Density process
3b. Discrete version of Girsanovs theorem. Conditionally Gaussian case
3c. Martingale property of the prices in the case of a conditionally Gaussian and logarithmically conditionally Gaussian distributions
3d. Discrete version of Girsanovs theorem. General case
3e. Integer-valued random measures and their compensators.Transformation of compensators under absolutely continuous changes of measures. Stochastic integrals.
3f. Predictable criteria of arbitrage-free (B， S)-markets
……
ChapterⅥ Theory of Pricing in Stochastic Financial Models. Discrete Time
1. European hedge pricing on arbitrage-free markets
2. American hedge pricing on arbitrage-free markets
3. Scheme of series of large arbitrage-free markets and asymptotic arbitrage
4. European options on a binomial (B， S)-market
5. American options on a binomial (B， S)-market
Chapter Ⅶ Theory of Arbitrage in Stochastic Financial Models.Continuous Time
1. Investment portfolio in semimartingale models
2. Semimartingale models without opportunities for arbitrage.Completeness
3. Semimartingale and martingale measures
4. Arbitrage， completeness， and hedge pricing in diffusion models of stock
5. Arbitrage， completeness， and hedge pricing in diffusion models of bonds
Chapter Ⅷ Theory of Pricing in Stochastic Financial Models.Continuous Time
1. European options in diffusion (B， S)-stockmarkets
2. American options in diffusion (B， S)-stoekmarkets.Case of an infinite time horizon
3. American options in diffusion (B， S)-stockmarkets.Finite time horizons
4. European and American options in a diffusion(B， P)-bondmarket
Bibliography
Index
Index of symbols
目 录内容简介
《随机金融概要(英文版)》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。
《随机金融概要(英文版)》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。
《随机金融概要(英文版)》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。
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