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
