应用模糊复合选择权於研发方案投资组合之研究

年理1177¹²¹理路100²理路100e-mail:[e-mail]力不流略利理論理不度度理理論理論年來益立來度立不researchanddevelopmentR&DnewproductdevelopmentNPD力NPD不不度理portfoliomanagement量略略strategicbalance降流不R&D理論fuzzycompoundoptions不理論qualitativepossibilitytheoryDuboisandPrade1999理不度理論度不數integerprogrammingmodel數不DixitandPindyck1994若R&D來利率paybackrates金流discountedcash-flownetpresentvalue略來不來金流不R&D年理1178年來realoptions理論financialtheory理innovationmanagementR&D類利Perlitzetal.1999利利BlackandScholes1973數log-normaldistribution率NPD流念量量Perlitzetal.1999量compoundoptions不Cooperetal.1998不益不來數Gaussian數來了便數來來金流流不CarlssonandFuller2003利益利略來略降益略略Cooperetal.1998略兩略度略度略度不Beaujonetal.2001略度略度參論NPD量不略NPDNPDNPD了略降不Beaujonetal.2001理論NPD力略度來益益力略數R&D力力量R&D流NPDNPD參數n數iv~i來數lB~l數ilC~il數ilkr~行ilk數數lkR~lk數數年理1179LjS~i略j數UjS~i略j數ijSI若i略j10ix若i10()()()()()()()(){}()61,05,~~4,~~3,~~2~~:Subjectto10,~~Max11111ixljSxCSIljSxCSIlkRxrlBxClxCviniLjiilijniUjiilijnilkiilkniliilniiili∀∈∀⋅⋅∀⋅⋅∀⋅∀⋅=−∑∑∑∑∑=====fppp1利來益益2不3數數45略略NPD不CarlssonandFuller2003Perlitzetal.1999R&D例()()()()7~/;,~/;,~~21212222111122aNeCTTbaMeCTTbaMeSrTrTT−−−−−=δν()[]()()()()()()()()[]()()()()()()11~10~2/~~/~ln9~8~2/~/~ln212222211121221TSbbTSTSrCESEbTSaaTSTSrSSEacσσσδσσσδ−=+−+=−=+−+=S~益數1~C數2~C數δdividendyield1T年理11802TcS()ρ,,baM累率ab聯數()aN累率()S~σ異數r利率()()()()()()()12,0~~12211212=−−−−−−CEcNeCEcNeSTTrTTcδ()()()()()()()()()14~13~2/~~/ln12121212221TTSccTTSTTSrCEScc−−=−−+−+=σσσδ益兩數便數異數CarlssonandFuller2003()()()[]()()()()().2464.62d112210βαβασαβγβγαγγ+++−+−=−++=−++−−=∫ababAbabaAE理論數理料歷料度不毎不參數度利DuboisandPrade1999理論數理論理不度不數數理論不數不度不j()15~~~~12111jnjjjbxaxaxa≤+++L若度理論()()1611122∑∑==−+≤+ninirjcjirijicijbbxaxaλλ()xµλ10jb~∑=niija1~∑=niicijxa12∑=niirijxa1λ()rjbλ−12cjbx年理1181()λ≥≤+++jnijjjbxaxaxa~~~~Nes2111L不念不1718()17Max111ininiliicixcxc∑∑==−γ()()1811111∑∑==−−≥−niljcjniilijicijbbxaxaλλ數NPD參數不例lmrm數ab度NPD度利理論理不度數理論度度0.9略度0.85度0.95度0.9略量略略1~3見略度0.7~0.99了51415181920度不不度料參Wangetal.2004略1略2略3lmrmab3124.643124.641029.81029.813,14,18,19,205,152,3,11不度度略1略2略30.714,18,19,205,10,152,3,40.814,18,19,205,10,153,40.8514,18,19,205,10,152,4,110.913,14,18,19,205,152,3,110.9514,18,19,205,10,152,3,110.9914,18,19,205,10,151,2,3論力R&DNPD不略年理1182度量理理力利益兩利理論不度料度數陸參1.Beaujon,G.J.,Marin,S.P.andMcDonald,G.P.(2001).BalancingandOptimizingaPortfolioofR&DProjects.NavalResearchLogistics,Vol.48,pp.18-40.2.Black,F.andScholes,M.(1973).ThePricingofOptionsandCorporateLiabilities.JournalofPoliticalEconomy.81,May-Jun,637.3.Carlsson,C.andFuller,R.(2003).Afuzzyapproachtorealoptionvaluation.FuzzySetsandSystems,139,pp.297-312.4.Cooper,R.G.,Edgett,S.J.andKleinschmidt,E.J.(1998).PortfolioManagementforNewProducts.Reading,MA:Perseus.5.Dixit,A.K.andPindyck,R.S.(1994).InvestmentunderUncertainty.PrincetonUniversityPress,Princeton,NJ.6.Dubois,D.,Prade,H.(1999).Qualitativepossibilitytheoryanditsapplicationstoconstraintsatisfactionanddecisionunderuncertainty.InternationalJournalofIntelligentSystems,Vol.14,No.1,pp.45-61.7.Geske,R.(1979).Thevaluationofcompoundoptions.JournalofFinancialEconomics,Vol.7,No.1,pp.63-81.8.Perlitz,M.,Peske,T.andSchrank,R.(1999).Realoptionsvaluation:thenewfrontierinR&Dprojectevaluation?R&DManagement,Vol.29,No.3,pp.255-269.9.Wang,J.,Hwang,W.L.andPeng,H.T.2004.AfuzzysetapproachforR&Dprojectselectionusingcompoundoptions-basedvaluatingmodel.TechnicalReport,Dept.ofIndustrialEngineering&SystemsManagement,FengChiaUniversity.