三、不确定情况下的投资决策

2••••••31•1.1–(Petersburgparadox)•·(Nicolaus,16951726)•A“”“”X2x•A•2-341•–•–•••––:105161•1.2––•1.3–-–72••vonNeumann–Morgenstern)]([)]([yUExUEyx≥⇔≥82•–Allaisparadox–PreferenceReversal•ABABA92•–PreferenceReversal–1•A28/3610•B3/36100–1102•–PreferenceReversal–1•A28/3610•B3/36100–2112•–TverskyandKahneman1981)•600•1200400•26002/36001/3122•–TverskyandKahneman1981)–•1200•26001/32/3•12=10943132•–TverskyandKahneman1981)–•1400•26001/32/3•12=3412114•AoccdrnigtoarscheearchatCmabrigdeUinervtisy,itdeosn’tmttaerinwahtoredrtheltteersinawrodare,theolnyiprmoetnttihngistahtthefristandlsatltteerbeattherghitpclae.Thersetcanbeatotalmsesandyoucansitllraeditwouthitaporbelm.Tihsisbcuseaethehuamnmniddeosnotraederveylteterbyistlef,butthewrodasawlohe.Amzanighuh.152•–TverskyandKahneman1981)•(framedependence)••162•––(certaintyeffect)–(reflectioneffect)–(isolationeffect)172•–•commonconsequence)1A(2500,0.33;2400,0.66;0,0.01)B(2400,1)N=72,A[18],B[82]1’C(2500,0.33;0,0.67)D(2400,0.34;0,0.66)N=72,C[83],B[17]182•–2A(40000.80)B(30001)N=95,A[20],B[80]2’C(-40000.80)D(-30001)N=95,C[92],D[8]192•–•••202•–375%25%A(30001)B(40000.80)N=141,A[74],B[26]3’C(30000.25)D(40000.2)N=141,C[42],D[58]212•–•3•3pseudo-certaintyeffect)3000222•–41000ABA(10000.50)B(5001)N=70,A[16],B[84]4’2000CDC(-10000.50)D(-5001)N=68,C[69],B[31]232•–•4•4242•–•Kahneman–Tversky(prospecttheory)–expectedutility)–Kahneman–Tverskyvaluefunction252•–Kahneman–Tversky(prospecttheory)•Kahneman–Tverskyvaluefunction•V•262•Kahneman–Tversky•KahnemanandTversky(1979)•Gainsandlossesareevaluatedfromasubjectivereferencepoint.Thefunctionrelatingthesubjectivevalueandthecorrespondinglossesissteeperthanthatforgains.•Asaresult,thedispleasureassociatedwiththelossisgreaterthanthepleasureassociatedwiththesameamountofgains.272ƒKahneman–Tversky(prospecttheory)„„20500„1049010••282ƒKahneman–Tversky(prospecttheory)„„292•Kahneman–Tversky•KahnemanandTversky(1979)302ƒKahneman–Tversky(prospecttheory)ƒ01„.„A.——17%7„B.——11%4„C.——41%17„D.——31%13„313.1•–0–0)1(21=−+hpph323.1•–––riskpremium:CD.–0010201020102()()(1)()(()(1)())()(1)()uWpuWhpuWhupWhpWhpuWhpuWh++−+⇒++−+++−+333.1BCADW0+h2W0W0+h1343.23.2.1••:•–)]~([)]~()~([wuEwwEUu=−π353.2BCADW0+h2W0W0+h1363.212U(z)=lnz0.85100.230373.23.2.2-••••E)~(W383.23.2.2-••]))W~E(())W~E(([212uuhPA′′′−=σπ393.23.2.2-•32-•4U(z)=lnz0.59.9100.510.1-403.23.2.3•))W~E(())W~E(()(uuWRA′′′=)W()W(uu′′′−413.23.2.3•-•–––423.23.2.3•–•–433.23.2.3•–––44Š''''''2''''2()()()[()]0()0[()]AdRzuzuzuzuzdzuz−+=≤⇒≥3.2453.23.2.3•––•–ik463.2•3.2.4•))W~E(()W~E(*))W~E((uu′′′−)W(*)(uWWu′′′−473.2•3.2.4••1•1•148000''''20''2''''2''/1(1)[()()][()()]1[()()][()()]1[()()](1){[()()]}|fffffffWdadWadadWaaWrEuWrraEuWrraEuWrrEuWWrraEuWrrsignsignEuWWrrηη−==++−+−=+−−−=+−−⇒−=−49000'''0'''((1)),((1)())((1)),()()((1))(())[()()]0()[()()]01RffRffRfffRffffRWrrrRWrarrRWrrruWWrrRWruWrrEuWrrEuWWrrη≥+≥++−+⇒−≤−+−−=⇒−⇒Q503.2•3.2.4•12513.3ŠRAŠW0(1+rf)RAŠRAŠikikikŠikik,,ikAARRz≥∀523.4ŠikŠikiŠikŠArrow-PrattikAARR≥''''''()()()()supinfiizkkzuzuzuzuz≥534two-fundmonetaryseparation•••544•cBzAzu)()(+=′BAzCBABAzCB−≤≥0,0,0,0],0max[,0,0BzAezu=′)(0,0,0≥zBA551()(),1(1)cABzuzCCB++=≠−+()ln()uzABz=+()exp{}AuzBzB=56W0j(1-)W0j[],,,,0maxmax()(1)(1(1))jjjjfjjjLEuαβλαβλλβααβ=+−=++−∑∑'0'0()()0,()(1)0,,1fjjjjjjEuWWrrEuWWrjβαβ−=−=∀=∑∑570((1(1)()))()0,CfjjfjfjEABWrrrrrjαβ⇒+++−−−=∀∑'0((1(1)()))()0fllfjflEuWrrrrrαβ++−−−=∑'()(),cuzABz=+'''0'0'''000'0''000'((1(1)()))()0,(1)(1)(1)(1)(1)(1)(1)(1)(1),CfjjfjfjfjjffjjfjjEABWrrrrrjABWrWWABWrABWrWWABWrjαβαβαβααβββ+++−−−=∀++⇒−=−++++⇒−=−=++⇒=∀∑∑Q585•stochasticdominance––:(n595•AB–-––XYXYX60••E(X)=E(Y)=2Var(X)=4Var(Y)=7==8/1,98/7,1Y2/1,42/1,0X561•145981187))((1421021))(()(××××=YuEXuExxu5625•—–∑=−=+−′′+−′+=3)(332)~)((!1)~)((21)~)(()()~(nnn•–Rothschild—Stiglitz––ABAF·BG·F1=G1=1[01]645•FSDfirst-orderstochasticdominance–:AABAB–uRRBAxdGxuxdFxuFSD≥≥∫∫)()()()(655ŠAB01FAFBŠ{}{}ABPrxPrx≥()(),[0,1]ABFxFxz≤∀∈66ŠAB11{0,1}0.0545ABPrr===×=14/51/2FB(x)13/41/4FA(x)11/20x1FB(x)FA(x)1F(x)0z67Š1.;2.()(),[0,1];3.,{0}1FSDABdABABFxFxzrrPαα≤∀∈=+≥=≥5683.AB[0,1]ABSSDAB≥569ŠŠBA0;[][],()(()())0,[0,1];,[]0SSDzABABdBAAABErErSzFxFxdxzrrErεε≥==−≤∀∈+=∫=[][],()()ABABSSDABErErVarrVarr≥⇒=≤570SSD+zFA(x)FB(x)z*1yF(x)0715•MSSDmonotonicsecond-orderstochasticdominance–ABAB72Š0;[][],()(()())0,[0,1];,[]0MSSDzABABdBAAABErErSzFxFxdxzrrErεε≥=−≤∀∈+≤≥∫=573•-––––••74•6.1–•••2'''22(),02()1,1/;()(),01(1)bUzzzbuzbzzbuzbdbbzbzbz=−=−=−==−−AARRdzu(z)0z1/b2()2buzzz=−75•6.2–•••0b'''2(),0()0;()0;lim()0;(),0bzbzbzzUzebuzbeuzbeuzdzb−−−→∞=−==−===AARRdzu(z)0z-1()bzuze−=−76•6.3–•••111'11''12(),0,0;1();1();11(),();10;0BBBBuzzzBBuzzuzzBzzzBBddzB−−−−−−=−==−===−=ARARRRRRdzdz77•6.4–•••,)(1)(11BBzABBzU−+−=],0max[,0,0BAzBA−≠78/A111'11''221()(),0,0,max[,0];1()();()();()1();0;()00;()();00;()00;BBBAuzABzBAzBBuzABzuzABzdzBzABzABzAdzzAzAABzABzA−−−−=+≠−−=+=−+==−++⇔===⇔=++⇔AARRRRdzRRdz