用L-矩方法擬合次指數(shù)分布計算股指在險價值.pdf

1、天津大學(xué)碩士學(xué)位論文用L矩方法擬合次指數(shù)分布計算股指在險價值姓名：高峰申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：史道濟(jì)2002.1.1ABSTRACTFinancialthneseriessuchasstockindexreturns，areofheavytailsAndsuchdatasetsarepoorlydescriptedbyaNormaldistribution，butpossiblycanbedonesobytheclas

2、sSofsubexponentialdistributionsAsanimportantclassofheavy—taileddistributions，subexponentialdistributionsCaDcharacterizetheskewnessandheavytails，SOtheyhavenowreceivedgreatattentioninfinanceSupposethatX，％areiidwithdfFDenot

3、ethepartialSUInofx1，，x。by又=Xlx。andtheirmaximumbyMn=max(Xl，，x。)TheintuitivecharacterisationofsubexponentialityiS：foralln≥2，P(S。x)～JD(％X)ThisimpliesthatthetailofthedftailofthedfofthemaximumMsofheavy—taileddistributionsz—00

4、ofthesumSnismainlydeterminedbytheThisisexactlyoneoftheintuitivenotionsIntheheavy—tailedcase，someoftheunderlyingdistributionsfailtohavetheexponentailmomentsrequiredforthestandardalgorithmsforthelight—tailedcaseThealternat

5、iveapproachcanturntoL。momentswhichareexpectationsofcertainlinearcombinationsoforderstatisticsL—momentscanbedefinedforanyrandomvariablewhosemeanexistsandformthebasisofaunifonlstatisticalinforencetheorywhichcoversthesummar

6、izationanddescriptionofthetheoreticalprobabilitydistributionsorobserveddatasamples，estimationofparametersandquantilesofprobabilitydistributions，andhypothesistestsforprobabilitydistributionsComparedwithconventionalmoments

7、，themainadvantageofL—momentsisthatL—momentsaremorerobusttooutliersinthedataThispapergivesthenecessarybackground，basicpropertiesandsomeessen。cialtheoreticalresultsonboththeclassSofsubexponentialdistributionsandthetheoryof

8、LmomentsByusingthemethodofLmoments，severalsubexponentia]distributions，includingthet，Log—normal，andWeibull，arefittedtostockindexreturnsfromShanghaiStockConsequently，theestimationofValue—at—Riskforthestockindexreturnsaredi