金融保險中重尾分布間的控制關系與跳時點過程的精致漸近性.pdf

1、蘇州大學碩士學位論文金融保險中重尾分布間的控制關系與跳時點過程的精致漸近性姓名：楊洋申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：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