關(guān)于幾類風(fēng)險模型的Gerber-Shiu函數(shù)的研究.pdf

1、分類號——學(xué)校代碼!=Q墨壘2學(xué)號至Q里!Q21QQ9墨墨關(guān)于幾類風(fēng)險模型的GerberShiu函數(shù)的研究TheR，esearchOfGerberShiuFunctionOnSeveralClassesRiskModels研究生姓名：胡燕指導(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)計研究方向：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五月ABSTRACTThedualriskmodelhasbeenresear

2、chwidelybothathomeandabroadinrecentyears，andtheobservationiscontinuousinthesemodelsHowever，thisassumptionistoestrictiveinapplicationsInordertogiveamorereasonabledescriptionoftheactuMbehaviorofthecompany，randomizedobserva

3、tionareintroducedtotheriskmodelInthisarticle，weconsiderthedualriskmodelwithinterestratesandjumpsunderrandomobservation，andstudyrelevantproblemsofbankruptcyInaddition，wediscusstheMarkovmodulatedriskmodelundermultilayerdiv

4、idendstrategyandobtainedsomeresultsoftheGerberShiudiscountedpenaltyfunctionThemainstructureofthepaperisasfollows：InChapter1，wesimplyintroducethebackgroundoftherisktheoryanditsdevelopmentInChapter2，elementarybasisofknowle

5、dgeandsomeriskmodelsarepresentedbrieflyInChapter3，onthebasisofthedualriskmodelwithinterest，wetakerandomizedobservationintoconsideration，obtainanewmodelAsystemofintegrodifferentialequationwithcertainboundaryconditionssati

6、sfiedbytheGerberShiudiscountedpenaltyfunctionarederivedItisdifficulttofindtheexplicitsolution，80weusetheSincmethodstoderiveaBapproximatesolutionInChapter4，wediscussthedualriskmodelwithtwosidedjumpsun—derrandomizedobserva

7、tion，andderiveasystemofintegrodifferentialequationwithcertainboundaryconditionssatisfiedbytheGerberShiudiscountedpenaltyfunctionWealsousetheSincmethodstoderiveanapproximatesolu—tionInChapter5，westudyaregimeswitchingriskm