连续进化金融模型与全局渐进化稳定策略

©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:3,,:410082,:[e-mail],,:410079;,:410003,:[e-mail]985(No104JJ3009)(No104YB062)KlausReinerSchenk2HoppSchenk2Hopp,Alchian(1950)Friedman(1953)Fama(1965),:,,,,,,:(),Shiller(1981),,,EvstigineevHensandSchenk2Hopp(2006),()(),,,,,,,:EvstigineevHensandSchenk2Hopp(2006),,,,:1;1420065©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2006),,Alchian(1950)Friedman(1953)Fama(1965),,,EvstigineevHensandSchenk2Hopp(2006),,,,t,K,(1),,(),Dkt,k=1,,K,t,p0t,,I,,,,,c0(),(),,,,=(ik)KI,Kk=1ik=1,0ik1,i=1,,I(1)(1-ct),ik(t)ik(1-ct)(2)ik,,i1-kk=1ik(t)=ct,(),,,,,1,,,,,twit,wt(w1t,,wIt),,k(t)(1k(t),,Ik(t)),k(1k,,Ik)itkit,k,it,k=ik(t)witk(t)wt=ikwitkwt(3),EvstigineevHensandSchenk2Hopp(2006),24:©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=Kk=1(p0t+tDkt+t+k(t)wt+t)it,k,i=1,,I(4)(perishable),,Ii=1Kk=1p0t+tDkt+tit,k=Ii=1ctwit+t3(5),1,Ii=1it,k=1(6),p0t+tDt+t=ctWt+t(7)Dt+tWt+tt+t,Dt+tKk=1Dkt+t,Wt+tIi=1wit+t3(8),,Wt+t,(),(4),,,,ritit,ritwitPWt,dkt+tkt+t,dkt+tDkt+tPDt+t,(4)(7)rit+t=Kk=1(ctdkt+t+k(t)rt+t)it,k,i=1,,I(9)rt+t=(r1t+t,,rIt+t)t+tt(it,k)Ik,,(9)rt+t=ct[Id-(1-ct)t]-1(tdt+t)(10)IdIt0,EvstigineevHensandSchenk2Hopp(2006)1,,[Id-(1-ct)t]-1,,,A(ai,j)IIt,zt(zit)I1tdt+t,Ii=1ai,j=1,j=1,,I,Ii=1zit=1(11)(I2),,,,,I=2,(10)1,r1t+t=1-r2t+tr2t+t=ctz3t-(ct-1)a2,1(a1,2+a2,1)+ct(a2,2-a2,1)(12)3420065©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=r1t,limt0+r2t+t=1-r1t=r2t3(13)(13),(19),,,:2(dkt)t0,k=1,,K,12r1t,r2t:dr1tdt=cz10-cr1ta1,2+a2,1=cKk=11kr1tdkt1kr1t+2k(1-r1t)-1Kk=11k2k1kr1t+2k(1-r1t)(14)dr2tdt=dr1tdt=cz20-cr2ta1,2+a2,1=cKk=12kr2tdkt1k(1-r2t)+2kr2t-1Kk=11k2k1k(1-r2t)+2kr2t(15)12,(14)(15),,(15),,(14)(15)ikik,,tk1k(1-r2t)+2kr2t,1,1k(1-r2t)+2kr2tk,pkt,(14)(15)dktpkt,;,,:1(15):1;1,,(15),22k,k=1,,K,c,,,,(14)(15),,,3r10,r20[0,1],r10+r20=101k1,02k1,k=1,,K,(14)(15){r1t,r2t}t0:44:©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=r10+ct0Kk=1dku1k1kr1u+2k(1-r1u)-1Kk=11k2k1kr1u+2k(1-r1u)r1udu(16)r2t=r20+ct0Kk=1dku2k1k(1-r1u)+2kr2u-1Kk=11k2k1k(1-r2u)+2kr2ur2udu(17),(16)(17)r1t+r2t=1,,(14)(15)():t,r1t=0,r2t=1r1t=1,r2t=0,r10,r20(0,1),r10+r20=1,0r1t,r2t1,,t0,r1t=1,r2t=0,(1,0),:t,r1t=1,r2t=03,:2ri0=0(1),i=1,2,t0,rit=0(1)();0ri01,i=1,2,t0,0rit1,,,,,,,:2i,ik,k=1,K,:ij,i,ri00,i1,limtrit=1i3,EvstigineevHensandSchenk2Hopp(2006),,,ri01,ri00,EvstigineevHensandSchenk2Hopp(2006),Evstigineev,HensandSchenk2Hopp(2005),,,,,,,,E=(dkt)dk,k=1,,K,Kk=1dk=1,0dk13(31,,3K),31d1,,3KdK,3,,3,G(1,2,x)cKk=1dk2k1k(1-x)+2kx-1Kk=11k2k1k(1-x)+2kxx(18):12=(21,,2K)3,x(0,5420065©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.),G(3,2,x)0(15)dr2tdt=G(3,2,r2t)+cKk=1(dkt-dk)2k1k(1-r2t)+2kr2tKk=11k2k1k(1-r2t)+2kr2tr2t(19)0r201,2,0r2t1,(19)1,(19)2,,t,r2t:4dkt,k=1,,K,(rit),i=1,21=3,21,0r20=1-r101,13,1,2,2limtr1t=1(m.s.),limtr2t=0(m.s.)(20)m.s.:(i),:,,,,,;(ii),,,;(iii),pkt=1kr1t+2kr2t(k=1,,K),,,:3:=(1,,K),,pkt=k,k=1,,K;3,:31=d1,,3K=dK,,,,pkt=dK=E(dkt),k=1,,K,,1,,,(1),,,,,3,,,3,,4,3,,1,,,,,,,,,64:©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:EvstigineevHensandSchenk2Hopp(2006),EvstigineevHensandSchenk2Hopp(2006),,EvstigineevHensandSchenk2Hopp(2006),Alchian(1950)Friedman(1953)Fama(1965),,,Merton(1990),YangandMa(2001),(2005),,,,,,,1Id-(1-ct)tctGrammer,I=2,(10)r1t+t=z1t(ct-1)a1,2z2t1+(ct-1)a2,211(ct-1)a2,11+(ct-1)a2,2r2t+t=1+(ct-1)a1,1z1t(ct-1)a2,1z2t11(ct-1)a2,11+(ct-1)a2,2(11)z1t+z2t=1,(12)(13),(12),limt0+r1t+t=a1,2a1,2+a2,1a1,2=Kk=11k2kkrtr1t,a2,1=Kk=11k2kkrt(1-r1t)a1,2+a2,1=Kk=11k2kkrt=a1,2r1t(13)2(12),LHopital,limt0r1t+t-r1tt=cz10-cr1ta1,2+a2,1(11)zt1(14),t1t+r2t=1,(15)3(14)(15),(16)(17),(14)(15),(15),f(X)cKk=1dkt2k1k(1-X)+2kX-1Kk=11k2k1k(1-X)+2kXX(A.1)7420065©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(15)dXdt=f(X),X0=r20[0,1](A.2),f()[0,1],f(0)=f(1)=0,r20[0,1],(A12)[0,1],Soong(1973)51112,f:L2Lipschitz:f(X)-f(Y)X-Y,0(A.3)L2[0,1]X(E[X2])1P2L2,Soong(1973),X,Y,0min(1k,2k)1k(1-X)+2kXmax(1k,2k),k=1,,K(A.4)0min(1k,2k)1k2k1k(1-X)+2kXmax(1k,2k),k=1,,K(A.5)|f(X)-f(Y)|cXKk=1dkt2k1k(1-X)+2kX-1Kk=11k2k1k(1-X)+2kX-Kk=1dkt2k1k(1-Y)+2kY-1Kk=11k2k1k(1-Y)+2kY+cKk=1dkt2k1k(1-Y)+2kY-1Kk=11k2k1k(1-Y)+2kY(X-Y)(A.6)mmin{1k,2k|k=1,,K},Mmax{1k,2k|k=1,,K}(A.7)(1)0mM1,,(A16)|f(X)-f(Y)|2cmM+c2MK4m|X-Y|,=2cmM+c2MK4m(A13)1:23x(0,1),H(3,2,x)Kk=1dk2kdk(1-x)+2kx-10,max21,,2KH(3,2,x)s.t.Kk=12k=102k1,k=1,,K(A.8),,,(A18),,2=3,H(3,3,x)=0,23x(0,1),H(3,2,x)H(3,3,x)=0(A18),L(2,)H(3,2,x)-Kk=12k-184:©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2,)9k=d2k(1-x)[dk(1-x)+2kx]2-=00,dk=dk(1-x)1-x+2kx,k=1,,K(A.9)k=1-x(A.10)(A110)(A19)2k=dk,k=1,,K2=32