欢迎来到天天文库
浏览记录
ID:7302185
大小:179.67 KB
页数:12页
时间:2018-02-11
《some classes of multivariate risk measures》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、SomeclassesofmultivariateriskmeasuresMartaCardinandElisaPaganiAbstract.Inactuarialliteraturethepropertiesofriskmeasuresorinsurancepremiumprin-cipleshavebeenextensivelystudied.Weproposeanewkindofstop-losstransformandarelatedorderinthemultivariatesettingandsomeequivalentconditions.I
2、nourworkthereisacharacterisationofsomeparticularclassesofmultivariateandbivariateriskmeasuresandanewrepresentationresultinamultivariateframework.Keywords:riskmeasures,distortionfunction,concordancemeasures,stochasticorders1IntroductionInactuarialsciencesitisfairlycommontocomparetw
3、orandomvariablesthatarerisksbystochasticorderingsdefinedusinginequalitiesonexpectationsoftherandomvariablestransformedbymeasurablefunctions.Bycharacterisingtheconsideredsetoffunctionssomeparticularstochasticorderingsmaybeobtainedsuchasstochasticdominanceorstop-lossorder.Thesestocha
4、sticorderrelationsofintegralformmaybeextendedtocoveralsothecaseofrandomvectors.Themaincontributionofthispaperconcernstheconstructionofamathematicalframeworkfortherepresentationofsomeclassesofmultivariateriskmeasures;inparticularwestudytheextensiontothemultivariatecaseofdistortedri
5、skmeasuresandweproposeanewkindofvectorriskmeasure.Moreover,weintroducetheproductstop-losstransformofarandomvectortoderiveamultivariateproductstop-lossorder.2MultivariatecaseWeconsideronlynon-negativerandomvectors.Let!bethespaceofthestatesofnature,Fbetheσ-fieldandPbetheprobabilityme
6、asureonF.OurrandomvectoristhefunctionX:!→RnsuchthatX(ω)representsthepayoffobtained+ifstateωoccurs.Wealsospecifysomenotations:FX(x):Rn→[0,1]isthedistributionfunctionofX,SX(x):Rn→[0,1]isitssurvivalortailfunction,and(X(ω)−a)+=max(X(ω)−a,0)componentwise.M.Corazzaetal.(eds.),Mathematic
7、alandStatisticalMethodsforActuarialSciencesandFinance©Springer-VerlagItalia201064M.CardinandE.PaganiAriskmeasure,orapremiumprinciple,isthefunctionalR:X→R˜,whereXisasetofnon-negativerandomvectorsandR˜istheextendedrealline.InwhatfollowswepresentsomedesirablepropertiesPforriskmeasure
8、s,thatareourproposaltogeneraliset
此文档下载收益归作者所有