精算学：理论与方法（英文版）

SinceactuarialeducationwasintroducedintoChinain1980s,moreandmoreattentionhavebeenpaidtothetheoreticalandpracticalresearchofactuarialscienceinChina.In1998,theNationalNaturalScienceFoundationofChinaapproveda1millionYuanRMBfinancialsupporttoakeyproject《InsuranceInformationProcessingandActuarialMathematicsTheory&Methodology》(project19831020),whichisthefirstkeyprojectonactuarialsciencesupportedbythegovernmentofChina.From1999to2003,professorsandexpertsfromFudanUniversity,PekingUniversity,InstituteofSoftwareofAcademiaSinica,EastChinaNormalUniversity,ShanghaiUniversityofFinanceandEconomics,ShanghaiUniversityandJinanUniversityworkedtogetherforthisproject,andachievedimportantsuccessesintheirresearchwork.Inasense,thisbookisasummationofwhattheyhadachieved.Thebookconsistsofsevenchapters.Chapter1mainlypresentsthemajorresultsaboutruinprobabilities,thedistributionofsurplusbeforeandafterruinforacompoundPoissonmodelwithaconstantpremiumrateandaconstantinterestrate.Thischapteralsogivesasymptoticformulasofthelowandupperboundsforthedistributionofthesurplusimmediatelyafterruinundersubexponentialclaims.Chapter2introducessomerecentresultsoncompoundriskmodelsandcopuladecomposition.Forthecompoundriskmodels,itincludestherecursiveevaluationofcompoundriskmodelsonmixedtypeseveritydistributioninone-dimensionalcase,thebivariaterecursiveequationonexcess-of-lossreinsurance,andtheapproximationtototallossofhomogeneousindividualriskmodelbyacompoundPoissonrandomvariable.Onthecopuladecomposition,theuniquenessofbivariatecopulaconvexdecompositionisproved,whilethecoefficientofthetermsinthedecompositionequationisgiven.Chapter3isconcernedwithdistortionpremiumprinciplesandsomerelatedtopics.Apartfromthecharacterizationofadistortionpremiumprinciple,thischapteralsoexaminestheadditivitiesinvolvedinpremiumpricingandrevealstherelationshipamongthethreetypesofadditivities.Furthermore,reductionofdistortionpremiumtostandarddeviationprincipleforcertaindistributionfamiliesisinvestigated.Inaddition,orderingproblemforreal-valuedrisks(beyondthenonnegativerisks)isaddressed,whichsuggeststhatitismorereasonabletoorderrisksinthedualtheorythantheoriginaltheory.Chapter4illustratestheapplicationoffuzzymathematicsinevaluatingandanalyzingrisksforinsuranceindustry.Asanexample,fuzzycomprehensiveevaluationisusedtoevaluatetheriskofsufferingfromdiseasesrelatedtobetterlivingconditions.Fuzzyinformationprocessing(includinginformationdistributionandinformationdiffusion)isintroducedinthischapterandplaysanimportantroleindealingwiththesmallsampleproblem.Chapter5presentssomebasicdefinitionsandprinciplesofFuzzySetTheoryandthefuzzytoolsandtechniquesappliedtoactuarialscienceandinsurancepractice.Thefieldsofapplicationinvolveinsurancegame,insurancedecision,etc.Chapter6isconcernedwithsomeapplicationsoffinancialeconomicstoactuarialmathematics,especiallytolifeinsuranceandpension.Combiningfinancialeconomics,actuarialmathematicswithpartialdifferentialequation,ageneralframeworkhasbeenestablishedtostudythemathematicalmodelofthefairvaluationoflifeinsurancepolicyorpension.Inparticular,analyticsolutionsandnumericalresultshavebeenobtainedforvariouslifeinsurancepoliciesandpensionplans.Chapter7providesaworkingframeworkforexploringtheriskprofileandriskassessmentofChinainsurance.Itisfortheregulatoryobjectiveofbuildingarisk-orientedsupervisionsystembasedonChinainsurancemarketprofileandconsistenttotheinternationaldevelopmentofsolvencysupervision.Theauthorsofvariouschaptersofthisbookare：ProfessorRongmingWangofEastChinaNormalUniversity(Chapter1),Dr.JingpingYangofPekingUniversity(Chapter2),Dr.XianyiWuofEastChinaNormalUniversity,Dr.XianZhouofHongKongUniversityandProfessorJinglongWangofEastChinaNormalUniversity(Chapter3),ProfessorHanjiShangofFudanUniversity(Chapter4),ProfessorYuchuLuofShanghaiUniversity(Chapter5),ProfessorWeixiShenofFudanUniversity(Chapter6)andProfessorZhigangXieofShanghaiUniversityofFinance&Economics(Chapter7).Astheeditor,Iammostgratefultoallauthorsfortheircooperation.IwouldliketothankProfessorTatsienLi,ProfessorZhongqinXuandProfessorWenlingZhang.Theirsupportisveryimportanttoourresearchworkandtothepublicationofthisbook.IalsothankMr.HaoWangforhiseffectiveworkineditingthebook.