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Continuous-time models

Author: Steven E Shreve
Publisher: New York, NY [u.a.] : Springer, 2004.
Edition/Format:   Print book : EnglishView all editions and formats

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions.


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Document Type: Book
All Authors / Contributors: Steven E Shreve
ISBN: 0387401016 9780387401010
OCLC Number: 177229554
Description: XIX, 550 S.
Contents: 1 General Probability Theory1.1 In.nite Probability Spaces1.2 Random Variables and Distributions1.3 Expectations1.4 Convergence of Integrals1.5 Computation of Expectations1.6 Change of Measure1.7 Summary1.8 Notes1.9 Exercises 2 Information and Conditioning2.1 Information and s-algebras2.2 Independence2.3 General Conditional Expectations2.4 Summary2.5 Notes2.6 Exercises 3 Brownian Motion3.1 Introduction3.2 Scaled Random Walks3.2.1 Symmetric Random Walk3.2.2 Increments of Symmetric Random Walk3.2.3 Martingale Property for Symmetric Random Walk3.2.4 Quadratic Variation of Symmetric Random Walk3.2.5 Scaled Symmetric Random Walk3.2.6 Limiting Distribution of Scaled Random Walk3.2.7 Log-Normal Distribution as Limit of Binomial Model3.3 Brownian Motion3.3.1 Definition of Brownian Motion3.3.2 Distribution of Brownian Motion3.3.3 Filtration for Brownian Motion3.3.4 Martingale Property for Brownian Motion3.4 Quadratic Variation3.4.1 First-Order Variation3.4.2 Quadratic Variation3.4.3 Volatility of Geometric Brownian Motion3.5 Markov Property3.6 First Passage Time Distribution3.7 Re.ection Principle3.7.1 Reflection Equality3.7.2 First Passage Time Distribution3.7.3 Distribution of Brownian Motion and Its Maximum3.8 Summary3.9 Notes3.10 Exercises 4 Stochastic Calculus4.1 Introduction4.2 Ito's Integral for Simple Integrands4.2.1 Construction of the Integral4.2.2 Properties of the Integral4.3 Ito's Integral for General Integrands4.4 Ito-Doeblin Formula4.4.1 Formula for Brownian Motion4.4.2 Formula for Ito Processes4.4.3 Examples4.5 Black-Scholes-Merton Equation4.5.1 Evolution of Portfolio Value4.5.2 Evolution of Option Value4.5.3 Equating the Evolutions4.5.4 Solution to the Black-Scholes-Merton Equation4.5.5 TheGreeks4.5.6 Put-Call Parity4.6 Multivariable Stochastic Calculus4.6.1 Multiple Brownian Motions4.6.2 Ito-Doeblin Formula for Multiple Processes4.6.3 Recognizing a Brownian Motion4.7 Brownian Bridge4.7.1 Gaussian Processes4.7.2 Brownian Bridge as a Gaussian Process4.7.3 Brownian Bridge as a Scaled Stochastic Integral4.7.4 Multidimensional Distribution of Brownian Bridge4.7.5 Brownian Bridge as Conditioned Brownian Motion4.8 Summary4.9 Notes4.10 Exercises 5 Risk-Neutral Pricing5.1 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 Motion5.3.2 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 Risk-Neutral Measure5.4.4 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 Coeffcients 5.5.3 Lump Payments of Dividends 5.5.4 Lump Payments of Dividends with Constant Coeffcients5.6 Forwards and Futures 5.6.1 Forward Contracts5.6.2 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
Responsibility: Steven E. Shreve.


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From the reviews of the first edition:"Steven Shreve's comprehensive two-volume Stochastic Calculus for Finance may well be the last word, at least for a while, in the flood of Master's level Read more...

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