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
2. Financial markets under uncertainty. C1assical theories of the dynamics of financial indexes, their critics and revision. Neoc1assical theories
3. Aims and problems of financial theory, engineering, and actuarial calcu1ations

Chapter Ⅱ Stochastic Models. Discrete Time
1. Necessary probabilistic concepts and several models of the dynamics of market prices
2. Linear stochastic models
3. Nonlinear stochastic conditionally Gaussian models
4. Supplement: dynamical chaos models

Chapter Ⅲ Stochastic Models. Continuous Time
1. Non-Gaussian models of distributions and processes.
2. Models with self-simi1arity. Fractality
3. Models based on a Brownian motion
4. Diffusion models of the evolution of interest rates, stock and bond prices
5. Semimartingale models

Chapter Ⅳ Statistical Analysis of Financial Data
1. Empirical data. Probabilistic and statistical models of their description. Statistics of 'ticks'.
2. Statistics of one-dimensional distributions
3. Statistics of vo1atility, corre1ation dependence and aftereffect in prices
4. Statistical R/S-analysis.

Part 2. Theory

Chapter V. Theory of Arbitrage in Stochastic Financial Models Discrete Time
1. Investment portfolio on a (B, S)-market
2. Arbitral:e-free market
3. Construction of martingale measures
by means of an absolutely continuous change ot measure
……
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