Stochastic Calculus for Finance II: Continuous-Time Models 金融随机计算II：边疆时间模型
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内容提要：
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. 作者简介：
Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education. 编辑推荐：
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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. 目录：
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 3.3 Brownian Motion 3.4 Quadratic Variation 3.5 Markov Property 3.6 First Passage Time Distribution 3.7 Reflection Principle 3.8 Summary 3.9 Notes 3.10 Exercises 4 Stochastic Calculus 4.1 Introduction 4.2 Ito's Integral for Simple Integrands 4.3 Ito's Integral for General Integrands 4.4 Ito-Doeblin Formula 4.5 Black-Scholes-Merton Equation 4.6 Multivariable Stochastic Calculus 4.7 Brownian Bridge …… 5 Risk-Neutral Pricing 6 Connections with Partial Differential Equations 7 Exotic Options 8 American Derivative Securities 9 Change of Numeraire 10 Term-Structure Models 11 Introduction to Jump Processes A Advanced Topics in Probability Theory B Existence of Conditional Expectations C Completion of the Proof of the Second Fundamental Theorem of Asset Pricing References Index |