utm chung k.l. aitsahlia f. elementary probability theory with stochastic processes and an introduction to mathematical finance (4ed springer 2006)

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1、DoobPolyaKolmogorovCramerBorelLevyKeynesFellerContentsPREFACETOTHEFOURTHEDITIONxiPROLOGUETOINTRODUCTIONTOMATHEMATICALFINANCExiii1SET11.1Samplesets11.2Operationswithsets31.3Variousrelations71.4Indicator13Exercises172PROBABILITY202.1Examplesofprobability202.2Definitionandillustrations242.3Deduct

2、ionsfromtheaxioms312.4Independentevents352.5Arithmeticaldensity39Exercises423COUNTING463.1Fundamentalrule463.2Diversewaysofsampling493.3Allocationmodels;binomialcoefficients553.4Howtosolveit62Exercises70viiviiiContents4RANDOMVARIABLES744.1Whatisarandomvariable?744.2Howdorandomvariablescomeabout

3、?784.3Distributionandexpectation844.4Integer-valuedrandomvariables904.5Randomvariableswithdensities954.6Generalcase105Exercises109APPENDIX1:BORELFIELDSANDGENERALRANDOMVARIABLES1155CONDITIONINGANDINDEPENDENCE1175.1Examplesofconditioning1175.2Basicformulas1225.3Sequentialsampling1315.4P´olya’su

4、rnscheme1365.5Independenceandrelevance1415.6Geneticalmodels152Exercises1576MEAN,VARIANCE,ANDTRANSFORMS1646.1Basicpropertiesofexpectation1646.2Thedensitycase1696.3Multiplicationtheorem;varianceandcovariance1736.4Multinomialdistribution1806.5Generatingfunctionandthelike187Exercises1957POISSONAN

5、DNORMALDISTRIBUTIONS2037.1ModelsforPoissondistribution2037.2Poissonprocess2117.3Frombinomialtonormal2227.4Normaldistribution2297.5Centrallimittheorem2337.6Lawoflargenumbers239Exercises246APPENDIX2:STIRLING’SFORMULAANDDEMOIVRE–LAPLACE’STHEOREM251Contentsix8FROMRANDOMWALKSTOMARKOVCHAINS2548.1Pr

6、oblemsofthewandererorgambler2548.2Limitingschemes2618.3Transitionprobabilities2668.4BasicstructureofMarkovchains2758.5Furtherdevelopments2848.6Steadystate2918.7Windingup(ordown?)303Exercises314APPENDIX3:MARTINGALE3259MEAN-VARIANCEPRICINGMODEL3299.1Aninvestmentsprimer3299.2Assetreturnandrisk33

7、19.3Portfolioallocation3359.4Diversification3369.5Mean-varianceoptimization3379.6Assetreturndistributions3469.7Stableprobabilitydistributions348Exercises351APPENDIX4:PARETOANDSTABLELAWS35510OPTIONPRICINGTHEORY35910.1Optionsbasics35910.2Arbitra