图书信息

内容简介

作者简介

目录

图书信息

书名：随机分析基础

出版社: 世界图书出版公司; 第1版 (2009年8月1日)

外文书名: elementary stochastic calculus with finance in view

平装: 212页

正文语种: 英语

开本: 24

isbn: 9787510005244, 7510005248

条形码: 9787510005244

商品尺寸: 22.2 x 14.8 x 1.2 cm

商品重量: 281 g

品牌: 世界图书出版公司北京公司

内容简介

《随机分析基础(英文版)》讲述了：Iknewbetter.Atthattime.staftmembersofeconomicsandmathematicsdepartmentsalreadydiscussedtheuseoftheBlackandScholesoptionpricingformula；coursesonstochasticfinancewere0fieredatleadinginstitutionssuchasETHZfirich.ColumbiaandStanford；andthereWasageneralagreementthatnotonlystudentsandstaftmembersofeconomicsandmathematicsde-partments、butalsopractitionersinfinanciaiinstitutionsshouldknowmoreaboutthisnewtopic.SoonIrealizedthatthereWasnotverymuchliteraturewhichcouldbeusedforteachingstochasticcaiculusataratherelementarylevel.Ialnfullyawareofthefactthatacombinationof“elementary”and“stochasticcalculus”isacontradictioniUitselfStochasticcalculusrequiresadvancedmathematicaitechniques；thistheorycannotbefullvunderstoodifonedoesnotknowaboutthebasicsofmeasuretheory，functionalanalysisandthetheoryofstochasticprocessesHowever.Istronglybelievethataninterestedpersonwhoknowsaboutelementaryprobabilitytheoryandwhocanhandletherulesofinte-grationanddifierentiationisabletounderstandthemainideasofstochasticcalculus.ThisissupportedbymyexperiencewhichIgainedincoursesforeconomicsstatisticsandmathematicsstudentsatVUWWellingtonandtheDepartmentofMathematicsinGroningen.IgotthesameimpressionasalecturerofcrashcoursesonstochasticcalculusattheSummerSchOOl.

作者简介

作者：(丹麦)麦考斯基

目录

Reader Guidelines

1 Preliminaries

1.1 Basic Concepts fl'om Probability Theory

1.1.1 Random Variables

1.1.2 Random Vectors

1.1.3 Independence and Dependence

1.2 Stochastic Processes

1.3 Brownian Motion

1.3.1 Defining Properties

1.3.2 Processes Derived from Brownian Motion

1.3.3 Simulation of Brownian Sample Paths

1.4 Conditional Expectation

1.4.1 Conditional Expectation under Discrete Condition

1.4.2 About a-Fields

1.4.3 The General Conditional Expectation

1.4.4 Rules for the Calculation of Conditional Expectations

1.4.5 The Projection Property of Conditional Expectations

1.5 Martingales

1.5.1 Defining Properties

1.5.2 Examples

1.5.3 The Interpretation of a Martingale as a Fair Game

2 The Stochastic Integral

2.1 The Riemann and Riemann-Stieltjes Integrals

2.1.1 The Ordinary Riemann Integral

2.1.2 The Riemann-Stieltjes Integral

2.2 The Ito Integral

2.2.1 A Motivating Example

2.2.2 The Ito Stochastic Integral for Simple Processes

2.2.3 The General Ito Stochastic Integral

2.3 The Ito Lemma

2.3.1 The Classical Chain Rule of Differentiation

2.3.2 A Simple Version of the Ito Lemma

2.3.3 Extended Versions of the Ito Lemma

2.4 The Stratonovich and Other Integrals

3 Stochastic Differential Equations

3.1 Deterministic Differential Equations

3.2 Ito Stochastic Differential Equations

3.2.1 What is a Stochastic Differential Equation?

3.2.2 Solving Ito Stochastic Differential Equations by the ItoLemma

3.2.3 Solving Ito Differential Equations via Stratonovich Calculus

3.3 The General Linear Differential Equation

3.3.1 Linear Equations with Additive Noise

3.3.2 Homogeneous Equations with Multiplicative Noise

3.3.3 The General Case

3.3.4 The Expectation and Variance Functions of the Solution

3.4 Numerical Solution

3.4.1 The Euler Approximation

3.4.2 The Milstein Approximation

4 Applications of Stochastic Calculus in Finance

4.1 The Black-Scholes Option Pricing Formula

4.1.1 A Short Excursion into Finance

4.1.2 What is an Option?

4.1.3 A Mathematical Formulation of the Option Pricing Problem

4.1.4 The Black and Scholes Formula

4.2 A Useful Technique: Change of Measure

4.2.1 What is a Change of the Underlying Measure?

4.2.2 An Interpretation of the Black-Scholes Formula by Change of Measure

Appendix

A1 Modes of Convergence

A2 Inequalities

A3 Non-Differentiability and Unbounded Variation of Brownian Sample Paths

A4 Proof of the Existence of the General Ito Stochastic Integral

A5 The Radon-Nikodym Theorem

A6 Proof of the Existence and Uniqueness of the Conditional Expectation

Bibliography

Index

List of Abbreviations and Symbols