破產(chǎn)時刻罰金折現(xiàn)期望的研究.pdf

1、分類號：!!竺密級：——單位代碼：!!!19學(xué)號：o!!!lI塑!!!!奪肥工學(xué)夫警HefeiUniversityofTechnology碩士學(xué)位論文MASTERnISSERTATION論文題目：學(xué)位類別：學(xué)科專業(yè)：(工程領(lǐng)域作者姓名：導(dǎo)師姓名：完成時間：②破產(chǎn)時刻罰金折現(xiàn)期望的研究學(xué)歷碩士應(yīng)用數(shù)學(xué)王后春杜雷樵教授2006年5月OntheExpectedDiscountedPenaltyatRuinAbstractAttheendofl

2、astcenturytheconceptionoftheexpecteddiscountedpenaltyfunctionatruinwasfirstintroducedbyHansUGerberandEliasSWShinwhoareeoutemporaryinternationalleadingexpertsatruintheoryAnumberofparticularcasesoftheexpecteddiscountedpena

3、ltyfunctionatruinledtoimportantquantitiesofinterestinrisktheoryTheseincludedtheprobabilityofultimateruin，theLaplacetransformofthetimeofruin，thejointandmarginaldistributionsandmomentsofthesurplusimmediatelybeforeruinandth

4、edeficitatruin，ereTheexpecteddiscountedpenaltyfuncdonatruinbeingapowerfulanalyticaltoolmadeitpossibletoanalyzethetimeofruin，thesurplusimmediatelybeforeruin，thedeficitatruin，andrelatedquantitiesinaunifiedmanner，Byvirtueof

5、studyingthepropertiesandtheapplicationoftheexpecteddiscountedpenaltyfunctionatruin，thisdissertationisdevotedtoachievingthreeaspectsofworkasfollows：1Intheclassicalriskmodel，HansUGerberandEliasSWShindiscussedthepropertieso

6、ftheexpecteddiscountedpenaltyfunctionatruininthecaseofConstantforceofinterest，andfromthisobtainedalotofnewresultsaboutthemodelOnthisbasis，WedescribetheinterestrandomnessbystandandWienerprocessandPoissonprocessandobminthe

7、renewalequationandtheasymptoticformulafortheexpecteddiscountedpenaltyfunctionatruininthissituationbyusingdifferentialargumentBymartingaleapproachwegetLundberg’sfundamentalequation，andfromthisderivetheprobabilityofultimat

8、eruinandtheprobabilitythatthesurplusreachesthegivenlevelSomeresultsinclassicalrisktheoryarealsodiscussedbyvirtueofthisrenewalequationIntheend，weobtainsomeresultsinthespecialcasewheretheclaimsizeobeystheexponentialdistrib

9、ution2ThecompoundPoissonriskmodelisconsideredinthepresenceofathresholddividendstrategyInthismodel，nodividendsarepaidiftheinsurer’Ssurplusisbelowcertainthresholdlevelanddividendsarepaidataconstantrate1essthanthepremiumrat

10、ewhenthesurplusisabovethisthresholdlevelAstothismodel，weobtaintheintegro—differentialequationandtheanalyticalexpressionfortheexpecteddiscountedpenaltyfunctionatruininthecaseofconstantforceofinterestTheseresultsareutilize