Essentials of stochastic finance : facts, models, theory / Albert N. Shiryaev ; translated from the Russian by N. Kruzhilin.

Translated from the unpublished Russian manuscript--Data sheet.

Includes bibliographical references (pages 803-824) and index.

Print version record.

Ch. I. Main concepts, structures, and instruments. Aims and problems of financial theory and financial engineering. 1. Financial structutes and instruments. 2. Financial markets underuncertainty. Classical theories of the dynamics of financial indexes, their critics and revision. Neoclassical theories. 3. Aims and problems of financial theory, engineering, and actuarial calculations. [symbol] -- ch. II. Stochastic models. Discrete time. 1. Necessary probabilistic concept and several models of the dynamics of market prices. 2. Linear stochastic models. 3. Nonlinear stochastic conditionally Gaussian models. 4. Supplement: dynamical chaos models -- ch. III. Stochastic models. Continuous time. 1. Non-Gaussian models of distributions and processes. 2. Models with self-similarity. Fractality. 3. Models based on a Brownian motion. 4. Diffusion models of the evolution of interest rates, stock and bond prices. 5. Semimartingale models. ch. 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 volatility, correlation dependence, and aftereffect in prices. 4. Statistical R/S-analysis. ch. V. Theory of arbitrage in stochastic financial models. Discrete time. 1. Investment portfolio on a (B, S)-market. 2. Arbitrage-free market. 3. Construction of martingale measures by means of an absolutely continuous change of measure. 4. Complete and perfect arbitrage-free markets -- ch. VI . 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 -- ch. 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 -- ch. 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)-stockmarkets. 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.

This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks.

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