29503.關(guān)于一類兩邊跳風(fēng)險模型的研究

1、密級關(guān)于一類兩邊跳風(fēng)險模型的研究TheResearchonTheRiskModelwithTwosidedJumps研究生姓名：熊院萍指導(dǎo)教師姓名、職稱：鄧迎春教授學(xué)科專業(yè)：概率論與數(shù)理統(tǒng)計研究方隨機過程及其應(yīng)用湖南師范大學(xué)學(xué)位評定委員會辦公室二零一四年三月ABSTRACTTheriskmodelwithtwosidedjumpshasbeenstudiedwidelyandgotgreatdevelopmentinrecentyear

2、sInthispaper，onthebasisofriskmodelwhichconsiderscurrentreservesandinterestrateofcompoundPoissonriskmodelandmarkovmodulatedriskmodel，wecombinethetwosidedjumpsriskmodel，obtaindifferentriskmodelswithrelatedcharacteristicsof

3、bankruptcyandsomeconclusionsThemainworkiSasfollows：Inchapter3，weconsidercurrentreservesandinterestrateriskmodelwithtwosidedjumpsAsweknown，intheclassicalriskmodel，theclaimsprocessiscompositePoissonprocessButintheactualope

4、rationsofsomecompanies，themoneythattoinvestmayearnorcompensate，thereforethegainscouldbepositiveornegativeismorerealisticAsystemofintegrodifferentialequationswithboundaryconditionssatisfiedbythemomentgeneratingfunction，th

5、enthmomentofthediscounteddividendpaymentspriortuinandthediscountedpenaltyfunction，arederived。Becausetheequationcoefficientisvariousandcomplicatedandit’8hardtofindthedisplaysolution，SOweusetheSincmeth—odstoderiveanapproxi

6、matesolution；wealsogetthegraphsofthediscounteddividendpaymentsandruinprobabilityInchapter4，wediscussthedualriskmodelwithtwosidedjumpsundertheMarkovregimeswitchingWeassumethatthedailyexpend，theclaimOCcurrenceandtheclaimam

7、ountareregulatedbyanexternalMarkovchainBycomputation，weobtaintheintegrodifferentialequationsofthediscounteddividendpaymentspriortuiningeneralcaseandintwostatesituation；besides，explicitsolutionstotheintegrodifferentialequ