随机金融概要
2010-2
世界图书出版公司
谢耶夫
834
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The author's intention was: to select and expose subjects that can be necessary or useful to those in-terested in stochastic calculus and pricing in models of financial markets operating under uncertainty; to introduce the reader to the main concepts, notions, and results of stochas-tic financial mathematics; to develop applications of these results to various kinds of calculations re-quired in financial engineering. The author considered it also a major priority to answer 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 r/sks. The subtitle "Facts, Models, Theory" appears to be an adequate reflection of the text structure and the author's style, which is in large measure a result of the 'feedback' with students attending his lectures (in Moscow, Ziirich, Aarhus,...).For instance, an audience of mathematicians displayed always an interest not only in the mathematical issues of the 'Theory', but also in the 'Facts', the par-ticularities of real financial markets, and the ways in which they operate. This has induced the author to devote the first chapter to the description of the key objects and structures present on these markets, to explain there the goals of finan-cial theory and engineering, and to discuss some issues pertaining to the history of probabilistic and statistical ideas in the analysis of financial markets. On the other hand, an audience acquainted with, say, securities markets and securities trading showed considerable interest in various classes of stochastic pro-cesses used (or considered as prospective) for the construction of models of the dynamics of financial indicators (prices, indexes, exchange rates, ... ) arid impor-tant for calculations (of risks, hedging strategies, rational option prices, etc.). This is what we describe in the second and the third chapters, devoted to sto-chastic 'Models' both for discrete and continuous time. The author believes that the discussion of stochastic processes in these chapters will be useful to a broad rahge of readers, not only to the ones interested in financial mathematics. We emphasize here that in the discrete-time case, we usually start in our de-scription of the evolution of stochastic sequences from their Doob decomposition into predictable and martingale components. One often calls this the 'martingale approach'. Regarded from this standpoint, it is only natural that martingale theory can provide financial mathematics and engineering with useful tools.
本书主要目的有三，一、研究随机分析必备内容以及不确定性下金融市场操纵模型中的估价；二、介绍主要概念、观点以及随机金融数学结果；三、讲述结果在金融工程各种计算中的应用。 本书为金融数学和工程数学的读者提供了概率统计的基本观点和随机分析市场风险的分析方法。书中不仅涵盖了金融中能够运用到的概率内容，也介绍了数学金融中的最新进展。既讲述了金融理论又结合金融实践，脉络清晰流畅。每部分的讲解从特殊到一般，从实例到结果。综合性强，包含了数学金融、熵以及马尔科夫理论。第二部分的学习需要对随机微积分知识有相当的了解。目次：第一部分：事实，模型：主要概念、结构和工具，金融理论目标和问题以及金融工程；随机模型，离散时间；随机模型，连续时间；金融数据统计分析；第二部分：理论：随机金融模型中的套利原理，离散时间；随机金融模型中的价格理论，离散时间；随机金融模型中的随意理论，连续时间；随机金融模型中的价格理论，连续时间。
作者:（俄罗斯）谢耶夫
ForewordPart 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' sequencesChapter Ⅲ Stochastic Models. Continuous TimeChapter Ⅳ Statistical Analysis of Financial DataChapter V. Theory of Arbitrage in Stochastic Financial Models Discrete TimeChapterⅥ Theory of Pricing in Stochastic Financial Models. Discrete Time Chapter Ⅶ Theory of Arbitrage in Stochastic Financial Chapter Ⅷ Theory of Pricing in Stochastic Financial Bibliography Index Index of symbols
插图：Central points there are the First and the Second fundamental asset pricingtheorems.The First theorem states （more or less） that a financial market is arbitrage-freeif and only if there exists a so-called martingale （risk-neutral） probability measuresuch that the （discounted） prices make up a martingale with respect to it. TheSecond theorem describes arbitrage-free markets with property of completeness,which ensures that one can build an investment portfolio of value replicatingfaithfully any given pay-off.Both theorems deserve the name fundamental for they assign a precise mathe-matical meaning to the economic notion of an 'arbitrage-free' market on the basisof （well-developed） martingale theory.In the sixth and the eighth chapters we discuss pricing based on the First and theSecond fundamental theorems. Here we follow the tradition in that we pay muchattention to the calculation of rational prices and hedging strategies for variouskinds of （European or American） options, which are derivative financial instru-ments with best developed pricing theory. Options provide a perfect basis for theunderstanding of the general principles and methods of pricing on arbitrage-freemarkets.Of course, the author faced the problem of the choice of 'authoritative' data andthe mode of presentation.
《随机金融概要(英文版)》是由世界图书出版公司出版的。
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此书值得推荐，无论学术，还是业界，都是一本好的参考书
专业书籍值得一读
需要数学基础较好的人读
不错，不过买了一年也就刚开始那段时间看了一点，需要很好的数理基础，外加耐心，否则买来就是砖头。。。