Stochastic Calculus for Finance II: Continuous-Time Models

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9780387401010: Stochastic Calculus for Finance II: Continuous-Time Models
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"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach...It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

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9781441923110: Stochastic Calculus for Finance Ii: Continuous-Time Models

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ISBN 10 :  144192311X ISBN 13 :  9781441923110
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Steven E. Shreve
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Description du livre Springer-Verlag New York Inc., United States, 2010. Hardback. Etat : New. 1st ed. 2004. Corr. 2nd printing 2010. Language: English . Brand New Book. A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach.It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance. --SIAM. N° de réf. du vendeur AAZ9780387401010

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Description du livre Springer-Verlag New York Inc., United States, 2010. Hardback. Etat : New. 1st ed. 2004. Corr. 2nd printing 2010. Language: English . Brand New Book. A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach.It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance. --SIAM. N° de réf. du vendeur AAZ9780387401010

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Description du livre Springer-Verlag New York Inc., 2004. HRD. Etat : New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. N° de réf. du vendeur GB-9780387401010

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Description du livre Springer-Verlag New York Inc., United States, 2010. Hardback. Etat : New. 1st ed. 2004. Corr. 2nd printing 2010. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach.It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance. --SIAM. N° de réf. du vendeur LIE9780387401010

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Description du livre Etat : New. Publisher/Verlag: Springer, Berlin | Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time.Master's level students and researchers in mathematical finance and financial engineering will find this book useful. | 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 It o's Integral for Simple Integrands4.2.1 Construction of the Integral4.2.2 Properties of the Integral4.3 It o's Integral for General Integrands4.4 It o-Doeblin Formula4.4.1 Formula for Brownian Motion4.4.2 Formula for It o 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 It o-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-Pay. N° de réf. du vendeur K9780387401010

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Shreve, Steven
Edité par Springer
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Description du livre Springer. Hardcover. Etat : New. 0387401016 Brand New ,Original Book , Direct from Source , Express 6-8 business days worldwide delivery. N° de réf. du vendeur RB#BF39139

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