2025年英語精算師考試題庫

一、單項選擇題（每題2分，共10題）1.Theword“actuary”isclosestinmeaningto______.A.accountantB.statisticianC.insuranceexpertD.financialadvisor2.Whichofthefollowingisacommonriskmeasureinactuarialscience?A.MeanB.MedianC.ValueatRiskD.Mode3.Thepresentvalueofasinglefuturecash-flowiscalculatedusingtheformula______.A.PV=FV/(1+r)^nB.PV=FV(1+r)^nC.PV=FV+rnD.PV=FV-rn4.Iftheannualinterestrateis5%,whatisthefuturevalueof$100after2years?A.$100(1+0.05)B.$100(1+0.05)^2C.$10020.05D.$100+0.0525.Thenormaldistributioniswidelyusedinactuarialworkbecause______.A.ItiseasytocalculateB.Manyreal-worlddatafollowthisdistributionC.IthasasinglepeakD.Alloftheabove6.Anactuaryismainlyconcernedwith______.A.PredictingfutureeventsandtheirfinancialimpactsB.DesigningmarketingstrategiesC.ConductinglegalresearchD.Buildingconstructionprojects7.Whichofthefollowingisanexampleofacontinuousrandomvariable?A.ThenumberofclaimsinayearB.ThetypeofinsurancepolicyC.ThetimebetweentwoconsecutiveclaimsD.Thenumberofinsuredpeople8.TheformulafortheexpectedvalueofadiscreterandomvariableXis______.A.E(X)=∑xP(X=x)B.E(X)=∫xf(x)dxC.E(X)=x+P(X=x)D.E(X)=xP(X=x)9.Ininsurance,theprincipleofindemnitymeans______.A.TheinsuredwillgetmorethantheactuallossB.TheinsuredwillgetlessthantheactuallossC.TheinsuredwillbecompensatedfortheactuallossD.Theinsuredwillnotbecompensated10.Thecoefficientofvariationiscalculatedas______.A.Standarddeviation/MeanB.Mean/StandarddeviationC.Variance/MeanD.Mean/Variance二、多項選擇題（每題2分，共10題）1.Whichofthefollowingareimportantskillsforanactuary?A.MathematicsB.StatisticsC.ProgrammingD.Communication2.Commontypesofinsurancethatactuariesworkwithinclude______.A.LifeinsuranceB.HealthinsuranceC.PropertyinsuranceD.Autoinsurance3.Whichofthefollowingaremeasuresofdispersion?A.RangeB.VarianceC.StandarddeviationD.Inter-quartilerange4.Inprobabilitytheory,mutuallyexclusiveeventshavethefollowingproperties______.A.P(A∩B)=0B.P(A∪B)=P(A)+P(B)C.P(A)P(B)=0D.Theycannotoccuratthesametime5.Actuariesusethefollowingmodelsintheirwork:A.MortalitymodelsB.InterestratemodelsC.ClaimfrequencymodelsD.Assetpricingmodels6.Thefactorsthatcanaffectthepremiumofaninsurancepolicyare______.A.RiskleveloftheinsuredB.CoverageamountC.PolicytermD.Marketcompetition7.Whichofthefollowingstatementsaboutcorrelationarecorrect?A.ItmeasuresthestrengthofthelinearrelationshipbetweentwovariablesB.Thevalueofcorrelationcoefficientrangesfrom-1to1C.Acorrelationof0meansthereisnorelationshipbetweenthetwovariablesD.Apositivecorrelationmeansthetwovariablesmoveinthesamedirection8.Infinancialmathematics,compoundinteresthasthefollowingcharacteristics:A.InterestisearnedonboththeprincipalandtheaccumulatedinterestB.ThefuturevalueformulaisFV=PV(1+r)^nC.ItleadstoexponentialgrowthoftheinvestmentD.Themorefrequentthecompounding,thehigherthefuturevalue9.Actuarialworkinvolvesthefollowingsteps:A.DatacollectionB.ModelbuildingC.RiskassessmentD.Pricingofinsuranceproducts10.Whichofthefollowingarenon-parametricstatisticalmethods?A.Wilcoxonrank-sumtestB.Kruskal-WallistestC.Chi-squaretestD.t-test三、判斷題（每題2分，共10題）1.Actuariesonlyworkintheinsuranceindustry.(False)2.Thevarianceofarandomvariableisalwaysnon-negative.(True)3.Inabinomialdistribution,theprobabilityofsuccessremainsthesameforeachtrial.(True)4.Thehigherthestandarddeviationofadataset,themorespreadoutthedatais.(True)5.Actuariesdonotneedtoconsidertheimpactofinflationintheircalculations.(False)6.Iftwoeventsareindependent,thenP(A∩B)=P(A)P(B).(True)7.Themeanofadatasetisalwaysequaltothemedian.(False)8.Inactuarialwork,modelsarealways100%accurateinpredictingfutureevents.(False)9.Thecoefficientofdetermination(R-squared)measuresthegoodness-of-fitofaregressionmodel.(True)10.Arisk-averseindividualwillalwayschoosetheoptionwiththelowestrisk.(True)四、簡答題（每題5分，共4題）1.Whatistheroleofanactuaryintheinsuranceindustry?Answer:Actuariesassessrisk,calculatepremiums,priceinsuranceproducts,andensurethefinancialstabilityofinsurancecompanies.Theyusedataandmodelstopredictfuturelossesandhelpcompaniesmanagetheirfinancialobligations.2.Explaintheconceptofpresentvalueinfinancialmathematics.Answer:Presentvalueisthecurrentworthofafuturesumofmoneyorcash-flow.Itiscalculatedbydiscountingthefutureamountusinganappropriateinterestrate.Ithelpsincomparingfutureandpresentfinancialamounts.3.Whatarethemaindifferencesbetweendiscreteandcontinuousrandomvariables?Answer:Discreterandomvariableshaveacountablenumberofpossiblevalues,likethenumberofclaims.Continuousrandomvariablescantakeonanyvaluewithinacertaininterval,suchastimebetweenclaims.4.Describetheprincipleofdiversificationinriskmanagement.Answer:Diversificationinvolvesspreadinginvestmentsorrisksacrossdifferentassetsorareas.Bydoingso,thenegativeimpactofoneriskyeventonthewholeportfoliocanbereducedasdifferentassetsmaynotallperformpoorlyatthesametime.五、討論題（每題5分，共4題）1.Discusstheimpactofemergingtechnologies(e.g.,artificialintelligence,bigdata)onactuarialwork.Answer:AIcanimproveriskassessmentbyanalyzinglargeamountsofdatamoreefficiently.Bigdataprovidesmoreinformationforaccuratemodels.However,italsobringschallengeslikedataprivacy.Actuariesneedtoadaptandusethesetoolstoenhancetheirwork.2.Howdoactuariesbalancetheneedforaccurateriskassessmentandtheaffordabilityofinsurancepremiums?Answer:Actuariesusesophisticatedmodelsforaccurateriskassessment.Tobalanceaffordability,theyconsidermarketcompetition,cost-effectiveness,andmayadjustpricingstrategies.Theyalsolookatd