欢迎来到天天文库
浏览记录
ID:7281723
大小:217.79 KB
页数:16页
时间:2018-02-10
《asset allocation under threat of a crash》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、CHAPTER67assetallocationunderthreatofacrashInthisChapter...•howtoallocateyourmoneytoaninvestmentwhenyouareworriedaboutamarketcrash67.1INTRODUCTIONThefollowingbyRalfKorn1andmyselfwasoriginallypublishedintheInternationalJournalofTheoreticalandAppliedFinance5171–188(2002).Weconsiderthedeterminationo
2、foptimalportfoliosunderthethreatofacrash.Ourmainassumptionisthatupperboundsforboththecrashsizeandthenumberofcrashesoccurringbeforethetimehorizonaregiven.Wemakenoprobabilisticassumptiononthecrashsizeorthecrashtimedistribution.Theoptimalstrategiesinthepresenceofacrashpossibilityarecharacterizedbyab
3、alanceproblembetweeninsuranceagainstthecrashandgoodperformanceinthecrash-freesituation.Explicitsolutionsforthelog-utilitycasearegiven.Ourmainfindingisthatconstantportfoliosarenolongeroptimalones.Itiswellknownthattheclassicallognormalstock/Black–Scholesmodelisnotabletoexplainlargejumpsinstockprices
4、appearinginreal-worldsecuritymarkets.Inparticular,itdoesnotcontainthepossibilityofacrashofthestockprices.Althoughthesecrashesarerareevents,theydooccurinreallife;theOctober1987crashbeingthelargestinrecentmemory.Therefore,thereisalongtraditionofmodelingjumpsinstockprices.Aseeminglyobviouscandidateo
5、faclassofsuitablestochasticprocessesisthatofjump-diffusionprocesses(seeMerton(1976)foranearlyreference).However,jump-diffusionapproachesonlyleadtostrategiesthathedgeacrashsituationinthemeanwhichisnorealprotectionagainsttheconsequencesofajumpatall.Inparticular,aninvestorfollowingsuchastrategywills
6、ufferlargelossesduringacrash.Asacontrast,byimplementingthestrategythatwewillproposeaninvestorneednotbeinfearofacrashasourstrategygiveshimfullprotectioninasensethatwillbemademorepreciseinthefollowingsections.AnalternativeformodelingcrashesisgiveninHuaandWilmott(1997).There,theunderlyingassumptions
7、arethatboththemaximalnumberofcrashesinagiventimeintervalandthebiggest1RalfKorn,FachbereichMathematik,UniversitatKaiserslautern,Germany¨korn@mathematik.uni-kl.de1062PartFiveadvancedtopicspossiblesizeofthecrashesareknown
此文档下载收益归作者所有