Brownian Motion Calculus布朗运动微积分
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作者： Ubbo Wiersema著
出 版 社：
出版时间： 2005-8-1字数：版次：页数： 313印刷时间： 2005/08/01开本： 32开印次：纸张： 胶版纸I S B N ： 9780470021705包装： 平装内容简介
There are not many calculus books that are very accessible to students without a strong mathematical background and the large majority of financial derivatives students do not have a strong quantitative background. This book provides a short introduction to the subject with examples of its use in mathematical finance e.g pricing of derivatives. Wiersma assumes only a basic knowledge of calculus and probability and guides the student through the book with examples and exercises (complemented by the website/disk). Wiersma has been teaching the subject for many years and the book will be based on his tried and tested course notes.
作者简介：
UBBO WIERSEMA was educated in Applied Mathematics at Delft, in Operations Research at Berkeley, and in Financial Economics and Financial Mathematics at the London School of Economics. He joined The Business School for Financial Markets (the ICMA Centre) at the University of Reading, UK, in 1997, to develop and teach its curriculum in Quantitative Finance. Prior to that, he was a derivatives mathematician at the merchant bank Robert Fleming in the City of London. His earlier career was in Operations Research in the US and Europe.
目录
Preface
1 Brownian Motion
1.1 Origins
1.2 Brownian Motion Specification
1.3 Use of Brownian Motion in Stock Price Dynamics
1.4 Construction of Brownian Motion from a Symmetric Random Walk
1.5 Covariance of Brownian Motion
1.6 Correlated Brownian Motions
1.7 Successive Brownian Motion Increments 1.7.1 Numerical Illustration
1.8 Features of a Brownian Motion Path
1.8.1 Simulation of Brownian Motion Paths
1.8.2 Slope of Path
1.8.3 Non-Differentiability of Brownian Motion Path
1.8.4 Measuring Variability
1.9 Exercises
1.10 Summary
2 Martingales
2.1 Simple Example
2.2 Filtration
2.3 Conditional Expectation
2.3.1 General Properties
2.4 Martingale Description
2.4.1 Martingale Construction by Conditioning
2.5 Martingale Analysis Steps
2.6 Examples of Martingale Analysis
2.6.1 Sum of Independent Trials
2.6.2 Square of Sum of Independent Trials
2.6.3 Product of Independent Identical Trials
2.6.4 Random Process B(t)
2.6.5 Random Process exp[B(t)
2.6.6 Frequently Used Expressions
2.7 Process of Independent Increments
2.8 Exercises
2.9 Summary
3 Ito Stochastic Integral
3.1 How a Stochastic Integral Arises
3.2 Stochastic Integral for Non-Random Step-Functions
3.3 Stochastic Integral for Non-Anticipating Random Step-Functions
3.4 Extension to Non-Anticipating General Random Integrands
3.5 Properties of an It6 Stochastic Integral
3.6 Significance of Integrand Position
3.7 It6 integral of Non-Random Integrand
3.8 Area under a Brownian Motion Path
3.9 Exercises
3.10 Summary
3.11 A Tribute to Kiyosi Ito
Acknowledgment
4 Ito Calculus
4.1 Stochastic Differential Notation
4.2 Taylor Expansion in Ordinary Calculus
4.3 Ito's Formula as a Set of Rules
4.4 Illustrations of Itp's Formula
4.4,1 Frequent Expressions for Functions of Two Processes
4.4.2 Function of Brownian Motion fiB(t)]
4.4.3 Function of Time and Brownian Motion f[t, B(t)]
……
5 Stochastic Differential Equations
6 Option Valuation
7 Change of Probability
8 Numeraire
A Annex A:Computations with Brownian Motion
B aNNEX B:Ordinary Integration
C Annex C:Brownian Motion Variability
D Annex D:Norms
E Annex E:Convergence Concepts
Answers to Exercises
References
Index
