Essentials of stochastic finance: facts, models, theory

Title\r......Page 4
Contents\r......Page 6
Foreword\r......Page 14
Part 1 Facts, Models\r......Page 18
1 Main Concepts, Structures, and Instruments\r......Page 19
1. Financial Structures and Instruments\r......Page 20
2. Financial Markets under Uncertainty.  Classical Theories of the Dynamics of Financial Indexes, their Crtiics and Revision.  Neoclassical Theories\r......Page 52
3. Aims and Problems of Financial Theory, Engineering, and Actuarial Calculations\r......Page 86
2 Stochastic Models.  Discrete Time\r......Page 97
1. Necessary Probabilistic Concepts and Several Models of the Dynamics of Market Prices\r......Page 98
2. Linear Stochastic Models\r......Page 134
3. Nonlinear Stochastic Conditionally Gaussian Models\r......Page 169
4. Supplement: Dynamical Chaos Models\r......Page 193
3 Stochastic Models.  Continuous Time\r......Page 205
1. Non-Gaussian Models of Distributions and Processes\r......Page 206
2. Models with Self-Similarity.  Fractality\r......Page 238
3. Models Based on a Brownian Motion\r......Page 253
4. Diffusion Models of the Evolution of Interest Rates, Stock and Bond Prices\r......Page 295
5. Semimartingale Models\r......Page 311
4 Statistical Analysis of Financial Data\r......Page 331
1. Empirical Data.  Probabilistic and Statistical Models of Their Description.  Statistics of \'Ticks\'\r......Page 332
2. Statistics of One-Dimensional Distributions\r......Page 344
3. Statistics of Volatility, Correlation Dependence, and Afereffect in Prices\r......Page 362
4. Statistical Methods of R/S-Analysis\r......Page 384
Part 2 Theory\r......Page 398
5 Theory of Arbitrage in Stochastic Financial Models.  Discrete Time\r......Page 399
1. Investment Portfolio on a (B,S)-Market\r......Page 400
2. Arbitrage-Free Market\r......Page 427
3. Construction of Martingale Measure by Means of an Absolutely Continuous Change of Measure\r......Page 450
4. Complete and Perfect Arbitrage-Free Markets\r......Page 498
6 Theory of Pricing in Stochastic Financial Models.  Discrete Time\r......Page 519
1. European Hedge Pricing on Arbitrage-Free Markets\r......Page 520
2. American Hedge Pricing on Arbitrage-Free Markets\r......Page 542
3. Scheme of Series of \'Large\' Arbitrage-Free Markets and Asymptotic Arbitrage\r......Page 570
4. European Options on a Binomial (B,S)-Market\r......Page 605
5. American Options on a Binomial (B,S)-Market\r......Page 625
7 Theory of Arbitrage in Stochastic Financial Models.  Continuous Time\r......Page 649
1. Investment Portfolio in Semimartingale Models\r......Page 650
2. Semimartingale Models without Opportunities for Arbitrage.  Completeness\r......Page 666
3. Semimartingale and Martingale Measures\r......Page 679
4. Arbitrage, Completeness, and Hedge Pricing in Diffusion Models of Stock\r......Page 721
5. Arbitrage, Completeness, and Hedge Pricing in Diffusion Models of Bonds\r......Page 734
8 Theory of Pricing in Stochastic Financial Models.  Continuous Time\r......Page 751
1. European Options in Diffusion (B,S)-Stockmarkets......Page 752
2. American Options in Diffusion (B,S)-Stockmarkets.  Case of an Infinite Time Horizon\r......Page 768
3. American Options in Diffusion (B,S)-Stockmarkets.  Finite Time Horizons\r......Page 795
4. European and American Options in a Diffusion (B,P)-Bondmarket......Page 809
Bibliography\r......Page 820
Index\r......Page 842
Index of Symbols\r......Page 850