隨機(jī)金融概要

前言

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.

內(nèi)容概要

　　本書主要目的有三，一、研究隨機(jī)分析必備內(nèi)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(diǎn)以及隨機(jī)金融數(shù)學(xué)結(jié)果；三、講述結(jié)果在金融工程各種計(jì)算中的應(yīng)用。　　本書為金融數(shù)學(xué)和工程數(shù)學(xué)的讀者提供了概率統(tǒng)計(jì)的基本觀點(diǎn)和隨機(jī)分析市場風(fēng)險(xiǎn)的分析方法。書中不僅涵蓋了金融中能夠運(yùn)用到的概率內(nèi)容，也介紹了數(shù)學(xué)金融中的最新進(jìn)展。既講述了金融理論又結(jié)合金融實(shí)踐，脈絡(luò)清晰流暢。每部分的講解從特殊到一般，從實(shí)例到結(jié)果。綜合性強(qiáng)，包含了數(shù)學(xué)金融、熵以及馬爾科夫理論。第二部分的學(xué)習(xí)需要對隨機(jī)微積分知識有相當(dāng)?shù)牧私?。目次：第一部分：事?shí)，模型：主要概念、結(jié)構(gòu)和工具，金融理論目標(biāo)和問題以及金融工程；隨機(jī)模型，離散時間；隨機(jī)模型，連續(xù)時間；金融數(shù)據(jù)統(tǒng)計(jì)分析；第二部分：理論：隨機(jī)金融模型中的套利原理，離散時間；隨機(jī)金融模型中的價格理論，離散時間；隨機(jī)金融模型中的隨意理論，連續(xù)時間；隨機(jī)金融模型中的價格理論，連續(xù)時間。

作者簡介

作者:（俄羅斯）謝耶夫

書籍目錄

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

章節(jié)摘錄

插圖：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.

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