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1111(Risk)12(Probability)(1)2000200570(2)2020002005(3)50(100)99801(ExpectedValue)nx1x2xnπ1π2πnnnniiixxxxxEππππ+++==∑=......)(221115010030602050()100X50+60X30+(50)580260100040100602000401400E1100060+10040640E2200060+(1400)40640?(Variance)nx1x2xnπ1,π2,……πn∑=−=−++−+−=∇niiinnxEXxEXxEXxEX1222221212)]([)]([......)]([)]([ππππ=−+−=∇%40*)640100(%60*)6401000(222=−−+−=∇%40*)6401400(%60*)6402000(222∇2∇=∇1RkRkσσddRK02XiE(x)iπ)),(,(iixExπ∇=∇RK=RK(),iixExπ),(,Exix0∂∂∇∂∂=∂∂iiXRKXRKσ0,0∂∂∇∂∇∂iXRKQiX0)()(∂∂∇∂∂=∂∂XRKXERKσ0)(,0∂∂∇∂∂XERKσQ,1......21=+++nπππ1nx1x2xnxiV(Xi)π1π2πn∑==+++=niiinnxVxVxVxVEU12211)()(......)()(ππππ11=∑=niiπ(ExpectedVtilityFunction)50(VonNeumann--MorgensternVtilityFunction)60xlV(x1)21X30x2V(x2)322XX−10x3V(x3)43XVN43322213211.0)(3.06.0)(*%10)(%30)(*%60XXXXXVXVXVEU+−+=++=21∑==niiiXVEU1)(π)(iiXVEU=∂∂πV0,)(iXiXiEUπ∂∂0,V0,)(iXiXiEUπ∂∂0,iiiiXXVXVEUXEU∂∂∂∂=∂∂)()()(iXVEU∂∂0iiXXV∂∂)(0iX)(iXVEU∂∂0iXiiXXV∂∂)(0iX)(iXVEU∂∂0iXEUiXiπ2ViX3EU1EU2EU1=EU2EU1=EU2(4)EU,EU1=EU2(5)EU1,EU2EU3,EU1EU2,EU2EU3,EU1EU3001(RishLover)2(RishEvader)3(RiskNeutral)1AViπiMiBVjπjMj+1iπjπEUiπiVjπjVME=iπiMjπjMV=V(M)100MV(M)V(M)ABV(M)100MEV(ME)EUEUV(ME)()()iπjπiMjMABijiijiMMMMVVVMW−−=−−)(WABM=EMiijijiEEVVVMMMMM+−−−=)()(WEMjjiiMMππ+)()1()()(ijijiijjiijijijjiiEVVMMMMVVVMMMMMMW−−−−=+−−−+=ππππ11iπjπiπjπiijjijjjjijjiijijijiEVVVVVVVVVVMMMMMWππππππ+=−+=+−=+−−−=)1()()()()(W(ME)=EU=iijjVVππ+MMEABEUV(M)W()=EUV(),EUV()EMEMEMV(M)0)(dMMdV,0)(22dMMVd,V0)(,0)('''MVM2V(M)W(ME)=EUV(ME),11-20)(dMMdV,0)(22dMMVd,V0)(,0)('''MVM3W(ME)=EU=V(ME),11-30)(dMMdV,0)(22=dMMVd,V0)(,0)('''=MVMV/V0'''V/V0'''V/V0'''?ll4MEEV()100()MFCDMEMF(Riskpremiu)(1nsurandMarket)?111EUCDMFMECD()19955000110011()04???199(99)10041090104100(100)0140100()H(Heart)()A(A11other)HA()HA2HA(ContingentCommodities)?1115()H()100?100HAa(EndowmentPoint)5050505050X04=20120b1000140=(100+100X04)C(?)100200l04A+O4H=140dAdH=04Wm()n()mA+nH(1+n)W()(111)252()131352=025()025()3952=075(1025=075)=Aπ025()075()Hπ105.025.0*175.0*4.04.0)1(=−=−=HAEππ15(1)haEHA***ππ=ahπ,Hππ=ππ−=1A04(1)a1163()005(1)0051?0a1/30.33075.0)1(*25.0**=+−=+ahaHAππ11033100A31H4003116B1Wmπn1-π0mπ+n(1-π)=0,ππ−=1nm,,,.,,mA+nH=(1+n)WπππWnnH1)1(+=+−,dA/dH=ππ−−1,B0aab()aB'aaha0?1160450Z0Za()(CenaintyLine)100XddB1-π(1-π)-13U1U2U1dU2fUlU2?fddffddf117118U3BlgdU3U4dgdggddgdB1U5B1d119U5B1-π(1π)-13U5B1dB1d0Z0Z0Z0ZBl119EPEQ0EEPEQ200Z(1)(2)0ZdB11110WEPEQ0EEPEQ∆311111B0B10Z1161191l61191112()aU0B1B0KB0aaB0AHeUoU1a100Hl()Al()H1UoUl100H1Al100UoU1()?100H2(ek)0100H2100H1?!1112AB1B0ahU0a()ahU0U11112BB1U0aaababU0U121113aU0B1a1000140U11113B1/Bi11-13C1114BlB0B00ZU1U2U2UIU2U1hU3U1U2U41115UoB1abbUlahU23BoB10Z1116B1a()abU1bahU2acU0(1)(2)(3)1r1r1rlr()r?πlπ1-rrE(R)(1π)r+(π(1r))=rπ(111)0(Fairlnsurance)rπ111(1)2wπwHAa11170W.1rr=πAπlπH1117ab=πbc=l-ππ1πacdrw=πww-wr=w-πw=(1π)wAHπ(1π)(1π)A+πH=(1π)W3?1171181l9dB10ZB1π(1π)d?dππ=(1π)wwπwwπw=(1)w(1π)w11180Zdefπ(1π)B1B1'B140ZU0dAMπwwU0U3U3U0U3U0U0?1119U0U1U1UOU0U11119U2()5wπLrwWlWlrwl1C1=WrWl1π2C2=W-L-rW1+W1π(1)w1π;1WlE=π(rWlW1)+(1π)rWl=(rπ)W1r=π(2)W1?E(W)=(1π)C1+πC2=(1π)(W-rW1)+π(W-L-rWl+W1)=wπL+W1(πr)=WπL(π=r)wIC1=C2WrW1WLrW1+W1W1LWlL=WWl=W(3)V=V(C)V1=V(C1)=V(WrWl)V2=V(C2)=V(WLrW1+W1)EU=(1π)V1+πV2=(1π)V(WrWl)+πV(WLrW1W1)W1EU.EU01=∂∂WEU0)1_1()1()1()1(=+−−∂∂−+−∂−−WrWLWVrrWWVVrππ)1()1()1()2(''ππ−−=rrCVCV112,11WrWLWCrWWC+−−=−=Qr=πV'(C2)=V'(C1)U'(W)0'C1=C2WrWi=WLrW1+W1W1=LEUWL=WW1=(R)0rπr(Unfairlnsurance)111E(R)0rππrE(R)0E(R)=r-πOrπE(R)=r-πOrπ11120B0B1(1π)WπWrWrπrwπw1120BlπW(1π)W=π(1π)B0rw(1π)W=r(1π)rπ(1π)A+rH=W(1π)(rπ)21121BoB1(1π)wπWrwrπrwπw1121B1π(1π)B0rw(1π)w=r(1π)rπ(1π)A+rH=w(1π)(rπ)31122B1B0U0U1U2U30Zbcdeπ(1π)UoaaB0B0Ulfagfgag?!iCUl?1123B1B0U2?B0BlB1112341124BlB0aU1aB0?U2B0Crwedd1l24U3U3B0()C?1125BlB0B1dU0B1UlewbrwbcbU2U2U0e?1126B1B0aU1U1aB0?B0eU2CU3U3UlaB01501127B0aUl()B0U2U2Ul10(1)(2)(3)(4)(1)(2)?iiXiπ∑==niiix1πµ1∑=ni1∑=−=∇niiix122)(µπ),(2∇=µUU∇U=U(µ,∇)µ∂∂/U00∂∇∂/U∂∇∂/U0∂∇∂/U=0x1xx=0x=l0xl1fµ∑==niiim1πµµmµiπ∇iiµm∑=−=∇niimim122)(πµµxxµ∇∑=++=niifixxx1])1([πµµµfmniniifiixxxxµµπµπµ)1()1(11−+=−+=∑∑==Q∑1ifπµinifixxxπµµ212])1([∑=−+=∇A2x∇2212212)(][mxxxxniiminiimi∇=−=−=∑∑==πµµππµµmxx∇=∇2UU(µ∇)Uµ()∇∇xµ∇Uxµxµ∇1128∇UA(())B(())U3U2UlxµxµMU∇MUxµx∇3x(01)x∇x=0∇xµx∇xµfµxm011-29Ax=lmxµµ=mxσσ=1129BABx)(fmmxfxµµµµ−∇∇+=C∇ABxABxµxxµx∇4112811291130UlABabax()bU3AB∇U3U2ABCxµxCCBCBCACAC?CU2ABCmfmxxdd∇−=∇µµµU2()??19521(1)(2)(3)nn1Vn)......,,,(321nµµµµµ=2(1)AB,ABABAB1(2)ABABBABABACovδδµµρ)(.=pABI)ρ0II)ρ0III)ρ=0ρABρ1ρ1|ρ|1ρρAB(3)()ρABABρ=05(4)AB()ADBD(5)(6)ABBD3ABCDe*EE=*σσ=4(1)()(2)(3)5(CAPMCapitalAssetsPricingModel)CAPM60601(1)1)2)3)4)5)6)(2)56-8CAPM(3)1)2)3)(4)FFR()FRRFKFHFRHFRRKRFRQ()R()1000030007000RRMR(5)1)FRHFMH.σσMFMFrErE−+=5.6-3EσE()MMσFr2)()((E-r))FrMFMσPσ(E-r)MFMσ(6)M(E-)iMσMFr2Mσ2MσMiMi2σσβ=5.6-4iMσiMi)()(2FMiFMMiMFirErErE−=−=−βσσ5.6-5)(FMiFirErE−+=βCAPMSMLiFr1iEMEiβMβPwlw2w3wnE(P)=w1E1+w2E2++wnEnw1(+())+w2(+())+…...wn(+())Fr1βMEFrFr2βMEFrFrnβMEFr=r+(w1+w2++wn)(r)F1β2βnβMEFE(P)=+()56-7FrPβMEFrP2(1)CAPMCAPM=PEFr+()PβMEFr(2)iriirMFrri+(r)+568FriαMFribiεiαbi0iiεiε0)(=iE