微观金融学及其数学基础

1(IOU)financeuncertaintyintertemporallyallocationRobinsonCrusoeriskproject/stochasticoptimalcontrolMerton1996continuous-timefinanceFridayMerton’sproblemreal-timestrategywarcraftageofempire2centralgovernment19561979208010%10%20%30%40%50%60%70%80%197019751979198019811982198319841985198619871988198919901197019902balancesheetclaimassetlangeO20301939publicgoods3GDP=C+IGDP|/22investmentcorporatefinancefinancialengineeringfinancialmarketfinancialeconomicsmoneybankingandeconomicsinternationalfinancepublicfinancemathematicalfinancefinancialeconometricsfinancialinnovations52capitalmarketmoneymarketderivatives34/microstructurecapitalstructure/profile/exchangeratediversification12exoticproductsErichberger&Harper1997LeRoy&Werner2001Obstfeld1992fractalgeometrychaostheory5MicrofinanceMacrofinanceDow&JonesBachelierL.MarkovitzD.ArrowDebreuTobinJ.SharpeW.SamulesonP.BlackF.ScholesM.MertonRC.HarrisonD.KrepsDuffieDHuangC.H.1870MarginSchoolMarshall.Anewclassicaleconomics2030MicrofinanceBasuetal2000RossS.A.1992NewPalgraveMelicher&Weshans1992institutiondescriptionrulesofthumb1992capitalidea199019976Keynsianrevolutionmicroeconomicsmacroeconomics1951Wicksell2050assetpricingRichardD.HumeD.MarxK.7//11M-M58/IS-LM/↓IS-LM-BP↓FisherI.1911PigouA.C1917;MarshallA.1923dichotomyHumeD1752purchasingpowerparityCasselG.1914LMIS-LM-Modell-Fleming1981permanentincomelifecircle19851999Obstfeld&Rogoff1996Turnovsky2000933CFA®CharteredFinancialAnalystCFP®CertifiedFinancialPlannerFRM®FinancialRiskManagerCandidateBodyofKnowledge103GabrielCrammer1728DanielBernouli17381870Wicksell20FisherI1906Hicks1934KenyesJ.M.1936Marschak19381938-Ramsey19272070——Arrow1953DebreuL.19593marketefficiencyClowesrandomwalk910Dunbar200012MertonR.C.19711973Breeden1979Bellman/ICAPMCCAPMcontinuous-timefinanceMerton1990BlackF.ScholesM.1973Europeanoptionself-financing-contingentclaimanalysisrealoptionnoarbitrageCox1976riskneutralHarrisonD.Paliska1979Kreps1981equivalentmartingalemeasure1938DoobmartingaleRadner19721985statesoftheworld196919711985a1985b1987diffusionprocess19971995-M-MCochrane2001xix13212KeynesJ.M.2180019001827172817381900190519061934193819001964192319381951-19471952195819631953M-M195919651975196519691971197319791973197519751966moppingup2behavioralfinanceexperimentaleconomics1-31-61419761985MonteCarloBoyle19771976&Pliska19791981Vasicek197719771985/&1989aKaratzas&Lehoczky&Shreve1987Ho&Lee1986Heath&Jarrow&Morton1992&1985inventingmoneyDunbar2000LongTermCapitalManagementLTCM1//23underlyingderivativesSundaresan2000154444Kochrane2001insight/16HullJ.C.1993measuretheory——121Newton16481729Leibniz16461716MarxK.Taylor16851731Langrange17361813Cauchy17891857Cayley1828189521617Laplace1933Kolmogorov19031987Borel18781956MarkowitzSethi1997Hicks1939Samuleson1947KuhnTucherDantzigBellman17Lebesgue18751941203——stochasticprocessBrownmotionIto1944DoobmartingaleHuntDynkinstoppingtime2090/NeftciS.NHullJ.C.1993——1902Cantor18451918Jordan18381922Neftci1996200018577891011115--1900MarkoviatzSethi1990199019MBArocketscience//Let’sbravethenewworldI1I2I/1111111211311412-1211221231241251313113213314141142143144APTCAPM1(bequest)(initialendowment)()2/1521-1I33(lifecircle)1)()2)3)4()(socialwelfare)()()1-1*Treasurybillcertificatesofdepositcommercialpaperbankers’acceptances(moneymarket)treasurybillcertificatesofdepositcommercialpaperbankers’acceptancesEurodollarsReposandReversesFederalFundsbrokers’call(fixedincomecapitalmarket)treasurybondsandnotesFederalagencydebt(municipalbonds)corporatebondMBSequitymarketcommonstockspreferredstockshumanresouseinvestment(asset)realestateclaim19%()31%34I446%324%13%52%0%10%20%30%40%50%60%70%80%90%100%1-1Miles,1996Allenetal200152%19%13%115111(commodity)6(utility)756(preference)56()——(numeraire)718I5(preferencerelation)(binaryrelation)8MMMR9xyz(commoditybundle)(consumebundle)(preferencerelation)(preferenceordering)1)yxf~()xyxxy2)yxfxxyyxyxff~⇔xyf~3)yx~xyyxyxf~~⇔xyf~(Axiom)10()111(completeness)∈yx,yxf~yxp~yx~tobeornottobe112(reflexivity)∈xxxf~113(transitivity)∈zyx,,yxf~zyf~zxf~~,ff~3(rational)(indifferentcurve)),(21CC=87197110I62Cxzy01C1-1114(Lexicographicpreference)),(21CC=),(21xxCCx=),(21yyCCy=1)yxCC11≥2)yxCC11≥yxCC22≥yxfAB115(continuity)xy}~|{yxxf}~|{yxxp}|{yxxf}|{yxxp11xy*x*xyf~x31)(indifferenceset)x}~:{xyy∈2)(uppercontourset)x}~:{xyyf∈3)(uppercontourset)x}~:{xyyp∈()),(yx()1171.27.1I72C01C1-2(desirability)(convexity)116(monotonicity)∈yx,yx≥yxf~117(strongmonotonicity)∈yx,yx≥yx≠yxf118(localnonsatiation)∈x0ε∈yε−||||yx12yxf119∈zyx,,zxf~zyf~)1,0(∈azyaaxf~)1(−+(diminishingmarginalratesofsubstitution)ab2Czxf~xyaax)1(−+zy01C2Czxf~xzyaax)1(−+y01Cab12ε−||||yxEuclidean7.3I81-3)(1Cx=)(2Cy=xyyx2121+1C2C1110(strictlyconvexity)∈zyx,,zxf