1、蘇州大學(xué)碩士學(xué)位論文金融保險(xiǎn)中重尾分布間的控制關(guān)系與跳時(shí)點(diǎn)過(guò)程的精致漸近性姓名：楊洋申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：概率論與數(shù)理統(tǒng)計(jì)指導(dǎo)教師：王岳寶20030401AbstractIIThedominantrelationsofheavytaileddistributionsandthepreciseasymptoticsforthepointprocessofthejumptimesofanextremalprocessininsurance

2、andfinanceAbstractInordertomeettheneedsofrecentresearchinAppliedProbabilitysuchasfinanceandinsurance，risktheoryrandomwalktheory，queueingtheoryandbranchingprocessesandSOon，theconceptsofheavy—tailedrandomvariables(orheavy—

3、taileddistributions)areintroducedTheyareoneoftheimportantobjectsmanyscholarsareconcernedonOntheotherhand，inariskprocess，thenumberoftheseheavytailedvariables’occurrenceuntilthetimet，ieallkindsofcountingprocess，isoneofthei

4、mportantobjects，whichmanyscholarsarestudyingThispapermainlydiscussesthedominantrelationsofheavy—taileddistributions，andthepreciseasymptoticsforthepointprocessofthejumptimesofanextremalprocessSincetherearetoomanysubclasse

5、sofheavytaileddistributionsandtheirrelationsareverycomplicated，inChap2ofthispaper，we’lldiscussthedominantrelationsofheavy—taileddistributions，andobtaintheequivalentconditionofthedistributionswhichCandominatealllight—tail

6、eddistributionsaswell88thoeewhichCandominatealllight—taileddistributionsandlightlyheavy—taileddistributions，inSection22InSection23，we’11discussthedominantrelationsbetweendistrbutionsandtheirCOrrespondingequilibriumdistri

7、butionsInthelastsectionofthischapterSection24，welllapplythedominantrelationsinthecloaureofsums；InChap3，we’lldiscussthepreciseasymptoticsWellintroducesomedefinitionsandSOmepreviousresultsinSection31，andintroducetheprecise

8、asymptoticsforthecountingprocessofrecordtimesofiidrvsinSection32，allofwhichextendandgeneralizethecorrespondingresultsinGut(2002)[19]Atlast，inSection33，we’IIemphasiz圯onthepreciseasymptoticsforthepointproce鋁ofthejumptimeso