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Essentials of stochastic finance : facts, models, theory

Essentials of stochastic finance : facts, models, theory (Loan 3 times)

Material type
단행본
Personal Author
Shiriaev, Al'bert Nikolaevich.
Title Statement
Essentials of stochastic finance : facts, models, theory / Albert N. Shiryaev ; translated from the Russian by N. Kruzhilin.
Publication, Distribution, etc
Singapore ;   River Edge, N.J. :   World Scientific ,   1999   (2008 printing)  
Physical Medium
xvi, 834 p. : ill. ; 23 cm.
Series Statement
Advanced series on statistical science & applied probability ; v. 3
ISBN
9810236050 9789810236052
General Note
Translated from the unpublished Russian manuscript--Data sheet.  
Bibliography, Etc. Note
Includes bibliographical references (p. [803]-824) and index.
Subject Added Entry-Topical Term
Investments -- Mathematics. Stochastic processes. Statistical decision. Financial engineering.
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020 ▼a 9789810236052
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050 0 0 ▼a HG4515.3 ▼b .S54 1999
082 0 0 ▼a 332.6/01/51923 ▼2 21
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100 1 ▼a Shiriaev, Al'bert Nikolaevich.
245 1 0 ▼a Essentials of stochastic finance : ▼b facts, models, theory / ▼c Albert N. Shiryaev ; translated from the Russian by N. Kruzhilin.
260 ▼a Singapore ; ▼a River Edge, N.J. : ▼b World Scientific , ▼c 1999 ▼g (2008 printing)
300 ▼a xvi, 834 p. : ▼b ill. ; ▼c 23 cm.
440 0 ▼a Advanced series on statistical science & applied probability ; ▼v v. 3
500 ▼a Translated from the unpublished Russian manuscript--Data sheet.
504 ▼a Includes bibliographical references (p. [803]-824) and index.
650 0 ▼a Investments ▼x Mathematics.
650 0 ▼a Stochastic processes.
650 0 ▼a Statistical decision.
650 0 ▼a Financial engineering.

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No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 332.601 S558e Accession No. 121167670 Availability Available Due Date Make a Reservation Service B M
No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Sejong Academic Information Center/Social Science/ Call Number 332.601 S558e Accession No. 151183830 Availability Available Due Date Make a Reservation Service

Contents information

Table of Contents


CONTENTS
Foreword = xiii
Part 1. Facts. Models = 1
  Chapter Ⅰ. Main Concepts, Structures, and Instruments. Aims and Problems of Financial Theory and Financial Engineering = 2
    1. Financial structures and instruments = 3
      1a. Key objects and structures = 3
      1b. Financial markets = 6
      1c. Market of derivatives. Financial instrumenets = 20
    2. Financial markets under uncertainty. Classical theories of the dynamics of financial indexes, their critics and revision. Neoclassical theories = 35
      2a. Random walk conjecture and concept of efficient market = 37
      2b. Investment portfolio. Markowitz's diversification = 46
      2c. CAPM : Capital Asset Pricing Model = 51
      2d. APT : Arbitrage Pricing Theory = 56
      2e. Analysis, interpretation, and revision of the classical concepts of efficient market. Ⅰ = 60
      2f. Analysis, interpretation, and revision of the classical concepts of efficient market. Ⅱ = 65
    3. Aims and problems of financial theory, engineering, and actuarial calculations = 69
      3a. Role of financial theory and financial engineering. Financial risks = 69
      3b. Insurance : a social mechanism of compensation for financial losses = 71
      3c. A classical example of actuarial calculations : the Lundberg-Cram e' r theorem = 77
  Chapter Ⅱ. Stochastic Models. Discrete Time = 80
    1. Necessary probabilistic concepts and several models of the dynamics of market prices = 81
      1a. Uncertainty and irregularity in the behavior of prices. Their description and representation in probabilistic terms = 81
      1b. Doob decomposition. Canonical representations = 89
      1c. Local martingales. Martingale transformations. Generalized martingales = 95
      1d. Gaussian and conditionally Gaussian models = 103
      1e. Binomial model of price evolution = 109
      1f. Models with discrete intervention of chance = 112
    2. Linear stochastic models = 117
      2a. Moving average model MA(q) = 119
      2b. Autoregressive model AR(p) = 125
      2c. Autoregressive and moving average model ARMA(p, q) and integrated model ARIMA(p, d, q) = 138
      2d. Prediction in linear models = 142
    3. Nonlinear stochastic conditionally Gaussian models = 152
      3a. ARCH and GARCH models = 153
      3b. EGARCH, TGARCH, HARCH, and other models = 163
      3c. Stochastic volatility models = 168
    4. Supplement : dynamical chaos models = 176
      4a. Nonlinear chaotic models = 176
      4b. Distinguishig between 'chaotic' and 'stochastic' sequences = 183
  Chapter Ⅲ. Stochastic Models. Continuous Time = 188
    1. Non-Gaussian models of distributions and processes = 189
      1a. Stable and infinitely divisible distributions = 189
      1b. L e' vy processes = 200
      1c. Stable processes = 207
      1d. Hyperbolic distributions and processes = 214
    2. Models with self-similarity. Fractality = 221
      2a. Hurst's statistical phenomenon of self-similarity = 221
      2b. A digression on fractal geometry = 224
      2c. Statistical self-similarity. Fractal Brownian motion = 226
      2d. Fractional Gaussian noise : a process with strong aftereffect = 232
    3. Models based on a Brownian motion = 236
      3a. Brownian motion and its role of a basic process = 236
      3b. Brownian motion : a compendium of classical results = 240
      3c. Stochastic integration with respect to a Brownian motion = 251
      3d. It o ^ processes and It o ^ 's formula = 257
      3e. Stochastic differential equations = 264
      3f. Forward and backward Kolmogorov's equations. Probabilistic representation of solutions = 271
    4. Diffusion models of the evolution of interest rates, stock and bond prices = 278
      4a. Stochastic interest rates = 278
      4b. Standard diffusion model of stock prices(geometric Brownian motion) and its generalizations = 284
      4c. Diffusion models of the term structure of prices in a family of bonds = 289
    5. Semimartingale models = 294
      5a. Semimartingales and stochastic integrals = 294
      5b. Doob-Meyer decomposition. Compensators. Quadratic variation = 301
      5c. It o ^ 's formula for semimartingales. Generalizations = 307
  Chapter Ⅳ. Statistical Analysis of Financial Data = 314
    1. Empirical data. Probabilistic and statiscal models of their description. Statistics of 'ticks' = 315
      1a. Structural changes in financial data gathering and analysis = 315
      1b. Geography-related features of the statistical data on exchange rates = 318
      1c. Description of financial indexes as stochastic processes with discrete intervention of chance = 321
      1d. On the statistics of 'ticks' = 324
    2. Statistics of one-dimensional distributions = 327
      2a. Statistical data discretizing = 327
      2b. One-dimensional distributions of the logarithms of relative price changes. Deviation from the Gaussian property and leptokurtosis of empirical densities = 329
      2c. One-dimensional distributions of the logarithms of relative price changes. 'Heavy tails' and their statistics = 334
      2d. One-dimensional distributions of the logarithms of relative price changes. Structure of the central parts of distributions = 340
    3. Statistics of volatility, correlation dependence, and aftereffect in prices = 345
      3a. Volatility. Definition and examples = 345
      3b. Periodicity and fractal structure of volatility exchange rates = 351
      3c. Correlation properties = 354
      3d. 'Devolatization'. Operational time = 258
      3e. 'Cluster' phenomenon and aftereffect in prices = 364
    4. Statistical R/S-analysis = 367
      4a. Sources and methods of R/S-analysis = 367
      4b. R/S-analysis of some financial time series = 376
Part 2. Theory = 381
  Chapter Ⅴ. Theory of Arbitrage in Stochastic Financial Models. Discrete Time = 382
    1. Investment portfolio on a (B, S)-market = 383
      1a. Strategies satisfying balance conditions = 383
      1b. Notion of 'hedging'. Upper and lower prices. Complete and incomplete markets = 395
      1c. Upper and lower prices in a single-step model = 399
      1d. CRR-model : an example of a complete market = 408
    2. Arbitrage-free market = 410
      2a. 'Arbitrage' and 'absence of arbitrage' = 410
      2b. Martingale criterion of the absence of arbitrage. First fundamental theorem = 413
      2c. Martingale criterion of the absence of arbitrage. Proof of sufficiency = 417
      2d. Martingale criterion of the absence of arbitrage. Proof of necessity(by means of the Esscher conditional transformation) = 417
      2e. Extended version of the First fundamental theorem = 424
    3. Construction of martingale measures by means of an absolutely continuous change of measure = 433
      3a. Main definitions. Density process = 433
      3b. Discrete version of Girsanov's theorem. Conditionally Gaussian case = 439
      3c. Martingale property of the prices in the case of a conditionally Gaussian and logarithmically conditionally Gaussian distributions = 446
      3d. Discrete version of Girsanov's theorem. General case = 450
      3e. Integer-valued random measures and their compensators. Transformation of compensators under absolutely continuous changes of measures. 'Stochastic integrals' = 459
      3f. 'Predictable' criteria of arbitrage-free(B, S)-markets = 467
    4. Complete and perfect arbitrage-free markets = 481
      4a. Martingale criterion of a complete market. Statement of the Second fundamental theorem. Proof of necessity = 481
      4b. Representability of local martingales. 'S-representability' = 483
      4c. Representability of local martingales('μ-representability' and '(μ-ν)-representability') = 485
      4d. 'S-representability' in the binomial CRR-model = 488
      4e. Martingale criterion of a complete market. Proof of necessity for d = 1 = 491
      4f. Extended version of the Second fundamental theorem = 497
  Chapter Ⅵ. Theory of Pricing in Stochastic Financial Models. Discrete Time = 502
    1. European hedge pricing on arbitrage-free markets = 503
      1a. Risks and their reduction = 503
      1b. Main hedge pricing formula. Complete markets = 505
      1c. Main hedge pricing formula. Incomplete markets = 512
      1d. Hedge pricing on the basis of the mean square criterion = 518
      1e. Forward contracts and futures contracts = 521
    2. American hedge pricing on arbitrage-free markets = 525
      2a. Optimal stopping problems. Supermartingale characterization = 525
      2b. Complete and incomplete markets. Supermartingale characterization of hedging prices = 535
      2c. Complete and incomplete markets. Main formulas for hedging prices = 538
      2d. Optional decomposition = 546
    3. Scheme of series of 'large' arbitrage-free markets and asymptotic arbitrage = 553
      3a. One model of 'large' financial markets = 553
      3b. Criteria of the absence of asymptotic arbitrage = 555
      3c. Asymptotic arbitrage and contiguity = 559
      3d. Some issues of approximation and convergence in the scheme of series of arbitrage-free markets = 575
    4. European options on a binomial(B, S)-market = 588
      4a. Problems of option pricing = 588
      4b. Rational pricing and hedging strategies. Pay-off function of the general form = 590
      4c. Rational pricing and hedging strategies. Markovian pay-off functions = 595
      4d. Standard call and put options = 598
      4e. Option-based strategies(combinations and spreads) = 604
    5. American options on a binomial(B, S)-market = 608
      5a. American option pricing = 608
      5b. Standard call option pricing = 611
      5c. Standard put option pricing = 611
      5d. Options with aftereffect. 'Russian option' pricing = 625
  Chapter Ⅶ. Theory of Arbitrage in Stochastic Financial Models. Continuous Time = 632
    1. Investment portfolio in semimartingale models = 633
      1a. Admissible strategies. Self-financing. Stochastic vector integral = 633
      1b. Discounting processes = 643
      1c. Admissible strategies. Some special classes = 646
    2. Semimartingale models without opportunities for arbitrage. Completeness = 649
      2a. Concept of absence of arbitrage and its modifications = 649
      2b. Martingale criteria of the absence of arbitrage. Sufficient conditions = 651
      2c. Martingale criteria of the absence of arbitrage. Necessary and sufficient conditions(a list of results) = 655
      2d. Completeness in semimartingale models = 660
    3. Semimartingale and martingale measures = 662
      3a. Canonical representation of semimartingales. Random measures. Triplets of predictable characteristics = 662
      3b. Construction of marginal measures in diffusion models. Girsanov's theorem = 672
      3c. Construction of martingale measeres for L e' vy processes. Esscher transformation = 683
      3d. Predictable criteria of the martingale property of prices. Ⅰ = 691
      3e. Predictable criteria of the martingale property of prices. Ⅱ = 694
      3f. Representability of local martingales('( Hc , μ-ν)-representability') = 698
      3g. Girsanov's theorem for semimartingales. Structure of the densities of probabilistic measures = 701
    4. Arbitrage, completeness, and hedge pricing in diffusion models of stock = 704
      4a. Arbitrage and conditions of its absence. Completeness = 704
      4b. Price of hedging in complete markets = 709
      4c. Fundamental partial differential equation of hedge pricing = 712
    5. Arbitrage, completeness, and hedge pricing in diffusion models of bonds = 717
      5a. Models without opportunities for arbitrage = 717
      5b. Completeness = 728
      5c. Fundamental partial differentai equation of the term structure of bonds = 730
  Chapter Ⅷ. Theory of Pricing in Stochastic Financial Models. Continuous Time = 734
    1. European options in diffusion(B, S)-stockmarkets = 735
      1a. Bachelier's formula = 735
      1b. Black-Scholes formula. Martingale inference = 739
      1c. Black-Scholes formula. Inference based on the solution of the fundamental equation = 745
      1d. Black-Scholes formula. Case with dividends = 748
    2. American options in diffusion(B, S)-stockmarkets. Case of an infinite time horizon = 751
      2a. Standard call option = 751
      2b. Standard put option = 763
      2c. Combinations of put and call options = 765
      2d. Russian option = 767
    3. American options in diffusion(B, S)-stockmarkets. Finite time horizons = 778
      3a. Special features of calculations on finite time intervals = 778
      3b. Optimal stopping problems and Stephan problems = 782
      3c. Stephan problem for standard call and put options = 784
      3d. Relations between the prices of European and American options = 788
    4. European and American options in a diffusion(B, P)-bondmarket = 792
      4a. Option pricing in a bondmarket = 792
      4b. European option pricing in single-factor Gaussian models = 795
      4c. American option pricing in single-factor Gaussian models = 799
Bibliograpgy = 803
Index = 825
Index of symbols = 833

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