圖書信息
出版社: 世界圖書出版公司; 第1版 (2010年2月1日)
外文書名: Essentials of Stochastic Finance: Facts, Models, Theory
平裝: 834頁
正文語種: 英語
開本: 24
ISBN: 7510005361, 9787510005367
條形碼: 9787510005367
尺寸: 22 x 14.8 x 3.6 cm
重量: 998 g
內容簡介
《隨機金融概要(英文版)》主要目的有三，一、研究隨機分析必備內容以及不確定性下金融市場操縱模型中的估價；二、介紹主要概念、觀點以及隨機金融數學結果；三、講述結果在金融工程各種計算中的套用。
《隨機金融概要(英文版)》為金融數學和工程數學的讀者提供了機率統計的基本觀點和隨機分析市場風險的分析方法。書中不僅涵蓋了金融中能夠運用到的機率內容，也介紹了數學金融中的最新進展。既講述了金融理論又結合金融實踐，脈絡清晰流暢。每部分的講解從特殊到一般，從實例到結果。綜合性強，包含了數學金融、熵以及馬爾科夫理論。第二部分的學習需要對隨機微積分知識有相當的了解。目次：第一部分：事實，模型：主要概念、結構和工具，金融理論目標和問題以及金融工程；隨機模型，離散時間；隨機模型，連續時間；金融數據統計分析；第二部分：理論：隨機金融模型中的套利原理，離散時間；隨機金融模型中的價格理論，離散時間；隨機金融模型中的隨意理論，連續時間；隨機金融模型中的價格理論，連續時間。
目錄
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
1. Non-Gaussian models of distributions and processes.
1a. Stable and infinitely divisible distributions
1b. Levy processes
1c. Stable processes
1d. hyperbolic distributions and processes
2. Models with self-simi1arity. Fractality
2a. Hurst's statistical phenomenon of self-simi1arity
2b. A digression on fractal geometry
2c. Statistical self-simi1arity. Fractal Brownian motion
2d. Fractional Gaussian noise: a process with strong aftereffect
3. Models based on a Brownian motion
3a. Brownian motion and its role of a basic process
3b. Brownian motion: a compendium of c1assical results
3c. Stochastic integration with respect to a Brownian motion
3d. It5 processes and ItS's formu1a
3e. Stochastic differential equations
3f. Forward and backward Kolmogorov's equations. Probabilistic representation of solutions
4. Diffusion models of the evolution of interest rates, stock and bond prices
4a. Stochastic interest rates
4b. Standard diffusion model of stock prices (geometric Brownian motion) and its generalizations
4c. Diffusion models of the term structure of prices in a family of bonds
5. Semimartingale models
5a. Semimartingales and stochastic integrals
5b. Doob-Meyer decomposition. Compensators. Quadratic variation
5c. itS's formu1a for semimartingales. Generalizations
Chapter Ⅳ Statistical Analysis of Financial Data
1. Empirical data. Probabilistic and statistical models of their description. Statistics of 'ticks'.
1a. Structural changes in financial data gathering and analysis
1b. Geography-re1ated features of the statistical data on exchange rates
1c. Description of financial indexes as stochastic processes with discrete intervention of chance
1d. On the statistics of 'ticks'
2. Statistics of one-dimensional distributions
2a.Statistical data discretizing
2b.One-dimensional distributions of the logarithms of re1ative price changes. Deviation from the Gaussian property
and leptokurtosis of empirical densities
2c.One-dimensional distributions of the logarithms of relative price changes. 'Heavy tails' and their statistics
2d.One-dimensional distributions of the logarithms of re1ative price changes. Structure of the central parts of distributions
3. Statistics of vo1atility, corre1ation dependence and aftereffect in prices
3a. Vo1atility. Definition and examples
3b. Periodicity and fractal structure of vo1atility in exchange rates
3c. Corre1ation properties
3d. 'Devo1atization'. Operational time
3e.'Cluster' phenomenon and aftereffect in prices
4. Statistical R/S-analysis.
4a. Sources and methods of R/S-analysis
4b. R/S-analysis of some financial time series
Part 2. Theory
Chapter V. Theory of Arbitrage in Stochastic Financial Models Discrete Time
1. Investment portfolio on a (B, S)-market
1a. Strategies satisfying ba1ance conditions
1b. Notion of 'hedging'. Upper and lower prices Complete and incomplete markets
1c. Upper and lower prices in a single-step model
1d. CRR-model: an example of a complete market
2. Arbitral:e-free market
2a. 'Arbitrage' and 'absence of arbitrage'
2b. Martingale criterion of the absence of arbitrage First fundamental theorem
2c. Martingale criterion of the absence of arbitrage Proof of sufficiency
2d. Martingale criterion of the absence of arbitrage Proof of necessity (by means of the Esscher conditional transformation)
2e. Extended version of the First fundamental theorem
3. Construction of martingale measures
by means of an absolutely continuous change ot measure
3a. Main definitions. Density process
3b. Discrete version of Girsanov's theorem. Conditionally Gaussian case
3c. Martingale property of the prices in the case of a conditionally Gaussian and logarithmically conditionally Gaussian distributions
3d. Discrete version of Girsanov's theorem. General case
3e. Integer-valued random measures and their compensators.Transformation of compensators under absolutely continuous changes of measures. 'Stochastic integrals'.
3f. 'predictable' criteria of arbitrage-free (B, S)-markets
……
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
