简介：Thispaperconsidersaclassofdelayedrenewalriskprocesseswithathresholddividendstrategy.ThemainresultisanexpressionoftheGerber-ShiuexpecteddiscountedpenaltyfunctioninthedelayedrenewalriskmodelintermsofthecorrespondingGerber-Shiufunctionintheordinaryrenewalmodel.Subsequently,thisrelationshipisconsideredinmoredetailinboththestationaryrenewalriskmodelandtheruinprobability.

简介：EmbrechtsandVeraverbekeinvestigatedtherenewalriskmodelandgaveatailequivalencerelationshipoftheruinprobabilities(?)(x)undertheassumptionthattheclaimsizeisheavy-tailed,whichisregardedasaclassicalresultinthecontextofextremalvaluetheory.Inthisnoteweextendthisresulttothedelayedrenewalriskmodel.

简介：Consideramultidimensionalrenewalriskmodel,inwhichtheclaimsizes{Xk,k≥1}formasequenceofindependentandidenticallydistributedrandomvectorswithnonnegativecomponentsthatareallowedtobedependentoneachother.Theunivariatemarginaldistributionsofthesevectorshaveconsistentlyvaryingtailsandfinitemeans.Supposethattheclaimsizesandinter-arrivaltimescorrespondinglyformasequenceofindependentandidenticallydistributedrandompairs,witheachpairobeyingadependencestructure.Apreciselargedeviationforthemultidimensionalrenewalriskmodelisobtained.