随机分析基础

Iknewbetter.Atthattime.staftmembersofeconomicsandmathematicsdepartmentsalreadydiscussedtheuseoftheBlackandScholesoptionpricingformula；coursesonstochasticfinancewere0fieredatleadinginstitutionssuchasETHZfirich.ColumbiaandStanford；andthereWasageneralagreementthatnotonlystudentsandstaftmembersofeconomicsandmathematicsde-partments、butalsopractitionersinfinanciaiinstitutionsshouldknowmoreaboutthisnewtopic.SoonIrealizedthatthereWasnotverymuchliteraturewhichcouldbeusedforteachingstochasticcaiculusataratherelementarylevel.Ialnfullyawareofthefactthatacombinationof“elementary”and“stochasticcalculus”isacontradictioniUitselfStochasticcalculusrequiresadvancedmathematicaitechniques；thistheorycannotbefullvunderstoodifonedoesnotknowaboutthebasicsofmeasuretheory，functionalanalysisandthetheoryofstochasticprocessesHowever.Istronglybelievethataninterestedpersonwhoknowsaboutelementaryprobabilitytheoryandwhocanhandletherulesofinte-grationanddifierentiationisabletounderstandthemainideasofstochasticcalculus.ThisissupportedbymyexperiencewhichIgainedincoursesforeconomicsstatisticsandmathematicsstudentsatVUWWellingtonandtheDepartmentofMathematicsinGroningen.IgotthesameimpressionasalecturerofcrashcoursesonstochasticcalculusattheSummerSchOOl.