有效证券市场的理性泡沫与股票内在价值的信息滤波

200644:100026788(2006)04200322121,2(11,350002;21,344000):;.,,.Kalman.:;;;Kalman:F83019;F832148;O29:ARationalBubbleinEfficientStockMarketsandtheInformationFilterofStockValueZOUHui2wen1,2(11SchoolofManagement,FuzhouUniversity,Fuzhou,Fujian350002,China;21SchoolofMathematicsandInformationScience,EastChinaInstituteofTechnology,Fuzhou,Jiangxi344000,China)Abstract:Theproducingconditions,measurementmethodsandformingreasonsoftherationalbubbleinefficientstockmarketswerediscussed.ThecorrespondingempiricalanalysisforthebubblesinChinesestockmarketwasmade.Onthebasisoftheabovestudies,theproblemreversedtothemeasurementofthebubblesinstockmarketswasdiscussed,i.e.,howtodistinguishstocksvaluefromthestockpriceswiththebubblesfiltered.ThemethodofKalmanfiltertofilterandforecasttheinformationofstocksvaluefromthestockpriceswasfirstintroduced.Keywords:stockvalue;noarbitrageassetprice;stockmarketbubble;Kalmaninformationfilter:2004210211:(2003034280),(03yi10):,(1959-),,,:.1,.,.199019941997,,.,,[1].,.,.Hamilton[2](1986);:.BlanchardFisher[3](1989),:(eliminatingbubble).FrootObstfeld[4](1991),:.BlanchardWatson[5](1982),.[6].:1),[1,4,713].;,,.2),[1423]...,,,[6].,,,,.,,,PtVtBt=Pt-Vt.,,,PtBtVt=Pt-Bt..:;.,Kalman,,.2211,,,,,,.,,,,.BlanchardWatson[5](1982),.,,,.,,,.,..:1),;;(,);2),;3);;4),.,,,Pt,dt,rf(),rf.,,,,,.,,.,,,,.,,,,.,,,:[24,25].(E(Pt+1|It)-Pt+E(dt+1|It))PPt=rf,(1)E(Pt+1|It),E(dt+1|It)tItt+1Pt+1dt+1()(,E(dt+1|It)dt).(1).(1)334Pt=aE(Pt+1|It)+aE(dt+1|It),(2)0a=1P(1+rf)1.(2),.ItIs,st.,E(E(Ps+1|Is)|It)=E(Ps+1|It),st,(3a)E(E(ds+1|Is)|It)=E(ds+1|It),st.(3b)t+k,(2)It,(3),E(Pt+k|It)=aE(Pt+k+1|It)+aE(dt+k+1|It),k=1,2,.(4)(4)(2),t+T,Pt=aTE(Pt+T|It)+Tk=1akE(dt+k|It).(5):,limTaTE(Pt+T|It)=0.(6)(6),T,(5),P3t=k=1akE(dt+k|It).(7),,,.P3t(2).P3t(6),(2).(6),(2).Pt=P3t+Bt.(8)(8)(2),(8)(2)P3t+Bt=aE(P3t+1|It)+aE(Bt+1|It)+aE(dt+1|It).E(Bt+1|It)=BtPa,(9)Bt.(9)E(Bt+k|It)=BtPak,k=1,2,.(10)0a1,k,Bt+klimkE(Bt+k|It)=limkBtPak=+,Bt0-,Bt0.(11),Bt,.,(8)(10)P3tBt.Bt,E(Bt+k|It)(k0),Bt(10),(2)(1),,,(rf),.21221211,P3t,,(1),.,Pt4320064P3t,.,Bt0,,P3t,.Bt0.,Bt=0,Pt=P3t.,,,,,.,,[19].,,,,..,,,(),,,,.,,.,.,,.,,.21212,,(10)E(Bk|I0)=B0Pak,k=1,2,(12)0.B00,,.E(Bk|I0)=B0PakB0Pak+1=E(Bk+1|I0),,P30,Bk,.,,.,,,,[26].,,PtP3t,,,,.,,,,..,,,,,,.21213,,,.,.BtBt+1=BtP(aq)+t+1,qt+1,1-q,(13)t+1,E(t+1|It)=0.(9),(9)E(Bt+1|It)=BtP(aq).(14)aaq,.534,1-q,q.,PtP3t.,(aq)-1-1a-1-1,.t+1,.0t,qt,t,,1-q,.,,,1-q,.,1-q,.,qt+1.,,,;,,.1-q,.,,,,,,[27].213P3t(7),E(dt+k|It)=dk,rf=r,P3tVt.Vt=k=t+1dkP(1+r)k-t=k=t+1ykP(1+r)k-t,(15)ykk,,dk=ykk.,Pt,(8)Pt=Vt+Bt.(16),Vt=P3t(1),Bt(9),Pt(1).,(1)Pt(),Bt..,.:,[21].,,,(1)()Pt[015Vt,2Vt].,Bt=hVt,-015h1.(17)(16),Bt=Pt-Vt.(18)t=BtPPt=(Pt-Vt)PPt,(19)t=BtPPt=hVtPPt,(20),Pt.,Vt,P3t.,Vt,.213116320064,Vt,Vt.,=1,.,,.t+1T,,.T+1,,,,,t+1T.(15)VtVt=Tk=t+1yk(1+r)k-t+€ytr(1+r)T-t.(21)€yt=Tk=t+1ykP(T-t).21312,,,,.,,,VtNt=Nt-1(1+rt)+Ft,(22a)Vt=NtPSt=Vt-1(1+rt)St-1PSt+FtPSt,(22b)Nt,rt,Ft,Stt,N0.214.11996199719981999200020012002Pt6.6707.7516.6677.60811.8796.0007.4511Vt3.7043.6463.6253.6033.5803.6363.814Bt2.9664.1053.0424.0058.2992.3643.637Bt0.9260.9110.9110.9010.8950.9090.954t0.4450.5300.4560.5260.6990.3940.488t0.1390.1180.1360.1180.0760.1510.1282Vt2.6192.9533.3833.7544.1022.9123.114Bt4.0524.7983.2843.8547.7773.0884.338Bt0.6550.7380.8460.9381.0250.7280.779t0.6070.6190.4930.5070.6550.5150.582t0.0980.0950.1270.1240.0870.1220.104Vt3.1623.303.5043.6793.8413.2743.464Bt3.4964.4523.1633.9308.0382.7263.988Bt0.7910.8250.8790.9200.960.8190.867t0.5260.5750.4750.5170.6770.4550.535t0.1190.1050.1320.1210.0820.1370.116:2002,,2002:,:=P,19962002.h[-015,1],h=0125.,7,r=41911%.€yt=Tk=t+1ykP(T-t)=011829.734,=1995=(P),N0=2337(301146P848142)=83013812().1.1,19962002():316583(01079)312622(015189),,.,,dk=yk=yk,,().,1.1,.1)1996,,19982001,50%,2000,265%,68%.,.2)1996,,14%.,,.3)2000,70%,812%,.1665122,19991186,86%;8639,19991113,13%;1999,0,0108%,199999%;282073148,199965%52%..2000,,,2001.4)19961999,,,.2000,,.,2001,.2002,.,.,(),().,,;,,.83200643311,PtVtBt=Pt-Vt.,,PtBtVt=Pt-Bt.,,[28].,.,.,,.,,..V(t)P(t)V(t)=(t-1)V(t-1)+(t-1),(23)P(t)=(t)V(t)+(t),(24)(t),(t),,,E[(t)]=E[(t)]=E[(t)(t)]=0,E[V(t)(s)]=E[V(t)(t)]=0,ts.E[(t)(s)]=tsQ(t),Q(t)0,E[(t)(s)]=tsR(t),R(t)0,ts=1,t=s0,ts.Kalman[29,30],,P(0),P(1),P(2),,P(T)V(t)^V(t)1)^V(t)=A(t)^V(t-1)+K(t)P(t)^V(0)=E[V(0)]=V0,t=1,2,,T.(25):A(t)=(t-1)R(t)[2(t)D(t-1)+R(t)]-1.K(t)Kalman,:K(t)=D(t-1)(t)[2(t)D(t-1)+R(t)]-1,D(t-1)=2(t-1)2(t-1)+Q(t-1).2(t),2(t)=R(t)D(t-1)[2(t)D(t-1)+R(t)]-12(0)=E[V(0)-^V(0)]2=20,V0,20.,(t)=P(t)-V(t)^(t)=P(t)-^V(t)=[1-K(t)]P(t)-A(t)^V(t-1).2)^V(t+1|t)=A1(t)^V(t|t-1)+K1(t)P(t)^V(0|-1)=^V(0)=E[V(0)]=V0,t=0,1,,T.(26):A1(t)=(t)R(t)[2(t)2(t|t-1)+R(t)]-1,K1(t)Kalman,:K1(t)=(t)2(t|t-1)(t)[2(t)2(t|t-1)+R(t)]-1.2(t+1|t),2(t+1|t)=(t)A1(t)2(t|t-1)+Q(t)(0|-1)=2(0)=E[V(0)-^V(0)]2=20,V0,20.,(t)=P(t)-V(t)^(t+1|t)=P(t)-^V(t+1|t)=[1-K1(t)]P(t)-A1(t)^V(t|t-1).312Q(t),R(t),(t),(t),(25)2(t)9342(t)=[R22(t-1)+RQ][222(t-1)+2Q+R]-12(0)=E[V(0)-^V(0)]2=20.(27){2(t)}.f(x)=(R2x+QR)P(22x+2Q+R),f(x)=R22P(22x+2Q+R)20,limxf(x)=RP2.f(x),0f(x)M,x(0,).2(t)=f(2(t-1)),2(t)-2(t-1)=f(2(t-1))-2