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．Classical theories of
the dynamics of financial indexes，their critics and revision
Neoclassical 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 classical concepts of efficient market
§2f．Analysis，interpretation，and revision of the classical conceDts of efficient market．II
3．Aims and problems offinancial theory，engineering， and actuarial calculations
§3a．Role of financial theory and financial engineering．Financial risks
§3b．Insurance：a social mechanism of compensation for financial 10sse8
§3c．A classical example of actuarial calculations：the Lundberg-Cramer theorem
Chapter II．Stochastic Models．Discrete Time
1．Necessary probabilistic concepts and several models of the dynamics of market prices
§1a．Uncertainty and irregularity 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 Ganssian models
§1e．Binomial model of price evolution
§1f．Models with discrete intervention of chance
2．Linear stochastic models
§2a．Moving average model MA(q)
§2b．Autoregressive model AR(p)
§2c．Autoregressive and moving average model ARMA(p，q) and integrated model ARIMA(p，d，q)
§2d．Prediction in linear models
3．Nonlinear stochastic conditionally Gaussian models
§3a．ARCH and GARCH models
§3b．EGARCH,TGARCH,HARCH,and other models
§3c．Stochastic volatility 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．Ldvy processes
§1c．Stable processes
§1d．Hyperbolic distributions and processes
2．Models with self-similarity．Fractality
§2a．Hurst’S statistical phenomenon of self-similarity
§2b．A digression on fractal geometry
§2c．Statistical sel5similarity．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
……
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

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数学中能够运用到的概率内容，也介绍了该领域的最新进展，内容包含金融数学、熵以及马尔科夫理论，全书理论与实践相结合，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。第二部分的学习需要对随机微积分知识有相当的了解。