Mathematical Techniques in Finance：Tools for Incomplete Markets 2009.pdf

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1、MathematicalTechniquesinFinanceMathematicalTechniquesinFinanceToolsforIncompleteMarketsSecondEditionAleˇsCern´yˇPrincetonUniversityPressPrincetonandOxfordCopyright
c2009byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:P

2、rincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedISBN:978-0-691-14121-3LibraryofCongressControlNumber:2009923897BritishLibraryCataloging-in-PublicationDataisavailableThisbookhasbeencomposedinTimesusingTEXTypesetandcopyeditedbyT&TProductionsLtd,LondonPrinted

3、onacid-freepaper∞press.princeton.eduPrintedintheUnitedStatesofAmerica10987654321Tomyparents,withloveGivemebutoneÞrmspotonwhichtostand,andIwillmovetheearth
oςµoιπo`υστ˜ωκα˜ικιν´ωτ˜ην `ην˜ArchimedesContentsPrefacetotheSecondEditionxiiiFromthePrefacetotheFirstEditionxix1TheSimplestModelofFinan

4、cialMarkets11.1One-PeriodFiniteStateModel11.2SecuritiesandTheirPayoffs31.3SecuritiesasVectors31.4OperationsonSecurities41.5TheMatrixasaCollectionofSecurities61.6Transposition61.7MatrixMultiplicationandPortfolios81.8SystemsofEquationsandHedging101.9LinearIndependenceandRedundantSecurities121

5、.10TheStructureoftheMarketedSubspace141.11TheIdentityMatrixandArrowÐDebreuSecurities161.12MatrixInverse171.13InverseMatrixandReplicatingPortfolios171.14CompleteMarketHedgingFormula191.15Summary201.16Notes211.17Exercises222ArbitrageandPricingintheOne-PeriodModel252.1HedgingwithRedundantSecur

6、itiesandIncompleteMarket252.2FindingtheBestApproximateHedge292.3MinimizingtheExpectedSquaredReplicationError322.4NumericalStabilityofLeastSquares342.5AssetPrices,ReturnsandPortfolioUnits362.6Arbitrage382.7No-ArbitragePricing402.8StatePricesandtheArbitrageTheorem412.9StatePricesandAssetRetur

7、ns442.10Risk-NeutralProbabilities452.11StatePricesandNo-ArbitragePricing462.12AssetPricingDuality472.13Summary482.14Notes492.15Appendix:LeastSquareswithQRDecomposition492.16Exercises52xContents3RiskandReturnintheOne-PeriodModel553.1UtilityFunctions563.2E