初等概率论（第4版）

图书标准信息

• 作者 [美]钟开莱 著
• 出版社 世界图书出版公司
• 出版时间 2010-01
• 版次 1
• ISBN 9787510004629
• 定价 45.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 402页
• 正文语种 英语
• 原版书名 Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance

【内容简介】

本书是一部介绍概率论及其应用的入门教程。其原始版本面世已经有30余年，但仍然是本科一二年级的经典概率教程。在第4版中增加了两章讲述应用和数学金融。传承前面版本详细、严谨的风格，讲述了有价证券和期货理论的基本知识。书中用最初等的方法讲述了概率测度、随机变量、分布以及期望等基本概念。离散和连续的案例都有所涉及，在讲述后者的时候运用了微积分知识。配以大量的典型例子重点讲述概率推理，集中介绍了组合问题、Poison过程、随机漫步、遗传模型和Markov链。每章末都附有习题及其解答。目次：集合；概率；计数；随机变量；附录。
读者对象：数学专业的本科生以及广大概率论爱好者。

【目录】

PREFACETOTHEFOURTHEDITION
PROLOGUETOINTRODUCTIONTOMATHEMATICALFINANCE
1SET
1.1Samplesets
1.2Operationswithsets
1.3Variousrelations
1.4Indicator
Exercises

2PROBABILITY
2.1Examplesofprobability
2.2Definitionandillustrations
2.3Deductionsfromtheaxioms
2.4Independentevents
2.5Arithmeticaldensity
Exercises

3COUNTING
3.1Fundamentalrule
3.2Diversewaysofsampling
3.3Allocationmodels;binomialcoefficients
3.4Howtosolveit
Exercises

4RANDOMVARIABLES
4.1Whatisarandomvariable?
4.2Howdorandomvariablescomeabout?
4.3Distributionandexpectation
4.4Integer-valuedrandomvariables
4.5Randomvariableswithdensities
4.6Generalcase
Exercises
APPENDIX1：BORELFIELDSANDGENERALRANDOMVARIABLES

5CONDITIONINGANDINDEPENDENCE
5.1Examplesofconditioning
5.2Basicformulas
5.3Sequentialsampling
5.4P61yasurnscheme
5.5Independenceandrelevance
5.6Geneticalmodels
Exercises

6MEAN，VARIANCE，ANDTRANSFORMS
6.1Basicpropertiesofexpectation
6.2Thedensitycase
6.3Multiplicationtheorem;varianceandcovariance
6.4Multinomialdistribution
6.5Generatingfunctionandthelike
Exercises

7POISSONANDNORMALDISTRIBUTIONS
7.1ModelsforPoissondistribution
7.2Poissonprocess
7.3Frombinomialtonormal
7.4Normaldistribution
7.5Centrallimittheorem
7.6Lawoflargenumbers
Exercises
APPENDIX2：STIRLINGSFORMULAANDDEMOIVRE-LAPLACESTHEOREM

8FROMRANDOMWALKSTOMARKOVCHAINS
8.1Problemsofthewandererorgambler
8.2Limitingschemes
8.3Transitionprobabilities
8.4BasicstructureofMarkovchains
8.5Furtherdevelopments
8.6Steadystate
8.7Windingup(ordown?)
Exercises
APPENDIX3：MARTINGALE

9MEAN-VARIANCEPRICINGMODEL
9.1Aninvestmentsprimer
9.2Assetreturnandrisk
9.3Portfolioallocation
9.4Diversification
9.5Mean-varianceoptimization
9.6Assetreturndistributions
9.7Stableprobabilitydistributions
Exercises
APPENDIX4：PARETOANDSTABLELAWS

10OPTIONPRICINGTHEORY
10.1Optionsbasics
10.2Arbitrage-freepricing：1-periodmodel
10.3Arbitrage-freepricing：N-periodmodel
10.4Fundamentalassetpricingtheorems
Exercises
GENERALREFERENCES
ANSWERSTOPROBLEMS
VALUESOFTHESTANDARDNORMALDISTRIBUTIONFUNCTION
INDEX