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金融隨機分析 第2卷

包郵 金融隨機分析 第2卷

作者:施瑞伍
出版社:世界圖書出版公司出版時間:2020-07-01
開本: 16開 頁數: 572
本類榜單:管理銷量榜
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金融隨機分析 第2卷 版權信息

  • ISBN:9787506272889
  • 條形碼:9787506272889 ; 978-7-5062-7288-9
  • 裝幀:一般膠版紙
  • 冊數:暫無
  • 重量:暫無
  • 所屬分類:>>

金融隨機分析 第2卷 內容簡介

《金融隨機分析》是一套隨機分析在定量經濟學領域中應用方面的有名教材,作者在該領域享有盛譽,全書共分2卷。
卷主要包括隨機分析的基礎性知識和離散時間模型;第2卷主要包括連續時間模型和該模型經濟學中的應用。就其內容而言,第2卷有較為實際的可操作性的定量經濟學內容,同時也包含了較為完整的隨機微分方程理論。本書各章有習題,適用于掌握微積積分基礎知識的大學高年級本科生和碩士研究生。

金融隨機分析 第2卷 目錄

1 General Probability Theory 1.1 Infinite Probability Spaces 1.2 Random Variables and Distributions 1.3 Expectations 1.4 Convergence of Integrals 1.5 Computation of Expectations 1.6 Change of Measure 1.7 Summary 1.8 Notes 1.9 Exercises 2 Information and Conditioning 2.1 Information and o-algebras 2.2 Independence 2.3 General Conditional Expectations 2.4 Summary 2.5 Notes 2.6 Exercises 3 Brownian Motion 3.1 Introduction 3.2 Scaled Random Walks 3.2.1 Symmetric Random Walk 3.2.2 Increments of the Symmetric Random Walk 3.2.3 Martingale Property for the Symmetric Random Walk 3.2.4 Quadratic Variation of the Symmetric Random Walk 3.2.5 Scaled Symmetric Random Walk 3.2.6 Limiting Distribution of the Scaled Random Walk 3.2.7 Log-Normal Distribution as the Limit of the Binomial Model 3.3 Brownian Motion 3.3.1 Definition of Brownian Motion 3.3.2 Distribution of Brownian Motion 3.3.3 Filtration for Brownian Motion 3.3.4 Martingale Property for Brownian Motion 3.4 Quadratic Variation 3.4.1 First-Order Variation 3.4.2 Quadratic Variation 3.4.3 Volatility of Geometric Brownian Motion 3.5 Markov Property 3.6 First Passage Time Distribution 3.7 Reflection Principle 3.7.1 Reflection Equality 3.7.2 First Passage Time Distribution 3.7.3 Distribution of Brownian Motion and Its Maximum 3.8 Summary 3.9 Notes 3.10 Exercises 4 Stochastic Calculus 4.1 Introduction 4.2 Ito's Integral for Simple Integrands 4.2.1 Construction of the Integral 4.2.2 Properties of the Integral 4.3 Ito's Integral for General Integrands 4.4 Ito-Doeblin Formula 4.4.1 Formula for Brownian Motion 4.4.2 Formula for Ito Processes 4.4.3 Examples 4.5 Black-Scholes-Merton Equation 4.5.1 Evolution of Portfolio Value 4.5.2 Evolution of Option Value 4.5.3 Equating the Evolutions 4.5.4 Solution to the Black-Scholes-Merton Equation 4.5.5 The Greeks 4.5.6 Put-Call Parity 4.6 Multivariable Stochastic Calculus 4.6.1 Multiple Brownian Motions 4.6.2 Ito-Doeblin Formula for Multiple Processes 4.6.3 Recognizing a Brownian Motion 4.7 Brownian Bridge 4.7.1 Gaussian Processes 4.7.2 Brownian Bridge as a Gaussian Process 4.7.3 Brownian Bridge as a Scaled Stochastic Integral 4.7.4 Multidimensional Distribution of the Brownian Bridge 4.7.5 Brownian Bridge as a Conditioned Brownian Motion 4.8 Summary 4.9 Notes 4.10 Exercises 5 Risk-Neutral Pricing 5.1 Introduction 5.2 Risk-Neutral Measure 5.2.1 Girsanov's Theorem for a Single Brownian Motion 5.2.2 Stock Under the Risk-Neutral Measure 5.2.3 Value of Portfolio Process Under the Risk-Neutral Measure 5.2.4 Pricing Under the Risk-Neutral Measure 5.2.5 Deriving the Black-Scholes-Merton Formula 5.3 Martingale Representation Theorem 5.3.1 Martingale Representation with One Brownian Motion 5.3.2 Hedging with One Stock 5.4 Fundamental Theorems of Asset Pricing 5.4.1 Girsanov and Martingale Representation Theorems 5.4.2 Multidimensional Market Model 5.4.3 Existence of the Risk-Neutral Measure 5.4.4 Uniqueness of the Risk-Neutral Measure 5.5 Dividend-Paying Stocks 5.5.1 Continuously Paying Dividend 5.5.2 Continuously Paying Dividend with Constant Coefficients 5.5.3 Lump Payments of Dividends 5.5.4 Lump Payments of Dividends with Constant Coefficients 5.6 Forwards and Futures 5.6.1 Forward Contracts 5.6.2 Futures Contracts 5.6.3 Forward-Futures Spread 5.7 Summary 5.8 Notes 5.9 Exercises 6 Connections with Partial Differential Equations 6.1 Introduction 6.2 Stochastic Differential Equations 6.3 The Markov Property 6.4 Partial Differential Equations 6.5 Interest Rate Models 6.6 Multidimensional Feynman-Kac Theorems 6.7 Summary 6.8 Notes 6.9 Exercises 7 Exotic Options 7.1 Introduction 7.2 Maximum of Brownian Motion with Drift 7.3 Knock-out Barrier Options 7.3.1 Up-and-Out Call 7.3.2 Black-Scholes-Merton Equation 7.3.3 Computation of the Price of the Up-and-Out Call 7.4 Lookback Options 7.4.1 Floating Strike Lookback Option 7.4.2 Black-Scholes-Merton Equation 7.4.3 Reduction of Dimension 7.4.4 Computation of the Price of the Lookback Option 7.5 Asian Options 7.5.1 Fixed-Strike Asian Call 7.5.2 Augmentation of the State 7.5.3 Change of Numeraire 7.6 Summary 7.7 Notes 7.8 Exercises 8 American Derivative Securities 8.1 Introduction 8.2 Stopping Times 8.3 Perpetual American Put 8.3.1 Price Under Arbitrary Exercise 8.3.2 Price Under Optimal Exercise 8.3.3 Analytical Characterization of the Put Price 8.3.4 Probabilistic Characterization of the Put Price 8.4 Finite-Expiration American Put 8.4.1 Analytical Characterization of the Put Price 8.4.2 Probabilistic Characterization of the Put Price 8.5 American Call 8.5.1 Underlying Asset Pays No Dividends 8.5.2 Underlying Asset Pays Dividends 8.6 Summary 8.7 Notes 8.8 Exercises 9 Change of Numeraire 9.1 Introduction 9.2 Numeraire 9.3 Foreign and Domestic Risk-Neutral Measures 9.3.1 The Basic Processes 9.3.2 Domestic Risk-Neutral Measure 9.3.3 Foreign Risk-Neutral Measure 9.3.4 Siegel's Exchange Rate Paradox 9.3.5 Forward Exchange Rates 9.3.6 Garman-Kohlhagen Formula 9.3.7 Exchange Rate Put-Call Duality 9.4 Forward Measures 9.4.1 Forward Price 9.4.2 Zero-Coupon Bond as Numeraire 9.4.3 Option Pricing with a Random Interest Rate 9.5 Summary 9.6 Notes 9.7 Exercises 10 Term-Structure Models 10.1 Introduction 10.2 Affine-Yield Models 10.2.1 Two-Factor Vasicek Model 10.2.2 Two-Factor CIR Model 10.2.3 Mixed Model 10.3 Heath-Jarrow-Morton Model 10.3.1 Forward Rates 10.3.2 Dynamics of Forward Rates and Bond Prices 10.3.3 No-Arbitrage Condition 10.3.4 HJM Under Risk-Neutral Measure 10.3.5 Relation to Afine-Yield Models 10.3.6 Implementation of HJM 10.4 Forward LIBOR Model 10.4.1 The Problem with Forward Rates 10.4.2 LIBOR and Forward LIBOR 10.4.3 Pricing a Backset LIBOR Contract 10.4.4 Black Caplet Formula 10, .4.5 Forward LIBOR and Zero-Coupon Bond Volatilities 10.4.6 A Forward LIBOR Term-Structure Model 10.5 Summary 10.6 Notes 10.7 Exercises 11 Introduction to Jump Processes 11.1 Introduction 11.2 Poisson Process 11.2.1 Exponential Random Variables 11.2.2 Construction of a Poisson Process 11.2.3 Distribution of Poisson Process Increments 11.2.4 Mean and Variance of Poisson Increments 11.2.5 Martingale Property 11.3 Compound Poisson Process 11.3.1 Construction of a Compound Poisson Process 11.3.2 Moment-Generating Function 11.4 Jump Processes and Their Integrals 11.4.1 Jump Processes 11.4.2 Quadratic Variation 11.5 Stochastic Calculus for Jump Processes 11.5.1 It6-Doeblin Formula for One Jump Process 11.5.2 Ito-Doeblin Formula for Multiple Jump Processes 11.6 Change of Measure 11.6.1 Change of Measure for a Poisson Process 11.6.2 Change of Measure for a Compound Poisson Process 11.6.3 Change of Measure for a Compound Poisson Process and a Brownian Motion 11.7 Pricing a European Call in a Jump Model 11.7.1 Asset Driven by a Poisson Process 11.7.2 Asset Driven by a Brownian Motion and a Compound Poisson Process 11.8 Summary 11.9 Notes 11.10 Exercises A Advanced Topics in Probability Theory A.1 Countable Additivity A.2 Generating o-algebras A.3 Random Variable with Neither Density nor Probability Mass Function B Existence of Conditional Expectations C Completion of the Proof of the Second Fundamental Theorem of Asset Pricing References Index
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金融隨機分析 第2卷 作者簡介

卡耐基·梅隆大學的計算金融MSCF項目是美國金融工程的帶頭者,歷史悠久,在華爾街亦享有盛譽。 本書作者Steven E.Shreve教授正是該項目的創辦人之一,他經常和華爾街大公司的負責人們溝通,了解行業內新的發展趨勢以在課程中加以改進,極大地促進了課程的優化。因而,由他所寫的《金融隨機分析》(第一、二卷)一直是隨機分析在數量金融領域應用方面的著名教材,許多世界名校將其作為金融工程專業的必修教材。

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