金融数学中的随机变分法

图书标准信息

• 作者 P·Malliavin、A·Thalmaier 著
• 出版社 世界图书出版公司
• 出版时间 2007-05
• 版次 1
• ISBN 9787506272957
• 定价 29.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 142页
• 正文语种 简体中文
• 丛书 金融数学名著

【内容简介】

stochaLsticCalculusofVariations(orMalliavinCalculus)consists，inbrief，inconstructingandexploitingnaturaldifferentiablestructuresonabstractDrobabilityspaces；inotherwords，StochasticCalculusofVariationsproceedsfromamergingofdifferentialcalculusandprobabilitytheory．AsoptimizationunderarandomenvironmentiSattheheartofmathemat’icalfinance，andasdifferentialcalculusiSofparamountimportanceforthesearchofextrema，itisnotsurprisingthatStochasticCalculusofVariationsappearsinmathematicalfinance．Thecomputationofpricesensitivities(orGreekslobviouslybelongstotherealmofdifferentialcalculus．
Nevertheless，StochasticCalculusofVariationsWasintroducedrelativelylateinthemathematicalfinanceliterature：firstin1991withtheOcone-Karatzashedgingformula，andsoonafterthat，manyotherapplicationsalDearedinvariousotherbranchesofmathematicalfinance；in1999anewirapetuscamefromtheworksofP．L．Lionsandhisassociates．

【目录】

1GaussianStochasticCalculusofVariations
1.1Finite-DimensionalGaussianSpaces，"HermiteExpansion
1.2WienerSpaceasLimitofitsDyadicFiltration
1.3Stroock-SobolevSpacesofFnctionalsonWienerSpace
1.4DivergenceofVectorFields，IntegrationbyParts
1.5ItSsTheoryofStochasticIntegrals
1.6DifferentialandIntegralCalculusinChaosExpansion
1.7Monte-CarloComputationofDivergence

2ComputationofGreeksandIntegrationbyPartsFormulae
2.1PDEOptionPricing;PDEsGoverningtheEvolutionofGreeks
2.2StochasticFlowofDiffeomorphisms;Ocone-KaratzasHedging
2.3PrincipleofEquivalenceofInstantaneousDerivatives
2.4PathwiseSmearingforEuropeanOptions
2.5ExamplesofComputingPathwiseWeights
2.6PathwiseSmearingforBarrierOption

3MarketEquilibriumandPrice-VolatilityFeedbackRate
3.1NaturalMetricAssociatedtoPathwiseSmearin
3.2Price-VolatilityFeedbackRate
3.3MeasurementofthePrice-VolatilityFeedbackRate
3.4MarketErgodicityandPrice-VolatilityFeedbackRate

4MultivariateConditioningandRegularityofLaw
4.1Non-DegenerateMaps
4.2Divergences
4.3RegularityoftheLawofaNon-DegenerateMap
4.4MultivariateConditioning
4.5RieszTransformandMultivariateConditioning
4.6ExampleoftheUnivariateConditioning

5Non-EllipticMarketsandInstabilityinHJMModels
5.1NotationforDiffusionsonRN
5.2TheMalliavinCovarianceMatrixofaHypoellipticDiffusion
5.3MalliavinCovarianceMatrixandHSrmanderBracketConditions
5.4RegularitybyPredictableSmearing
5.5ForwardRegularitybyanInfinite-DimensionalHeatEquation
5.6InstabilityofHedgingDigitalOptionsinHJMModels
5.7EconometricObservationofanInterestRateMarket

6InsiderTrading
6.1AToyModel：theBrownianBridge
6.2InformationDriftandStochasticCalculusofVariations
6.3IntegralRepresentationofMeasure-ValuedMartingales
6.4InsiderAdditionalUtility
6.5AnExampleofanInsiderGettingFreeLunches

7AsymptoticExpansionandWeakConvergence
7.1AsymptoticExpansionofSDEsDependingonaParameter
7.2WatanabeDistributionsandDescentPrinciple
7.3StrongFunctionalConvergenceoftheEulerScheme
7.4WeakConvergenceoftheEulerScheme

8StochasticCalculusofVariationsforMarketswithJumps
8.1ProbabilitySpacesofFiniteTypeJumpProcesses
8.2StochasticCalculusofVariationsforExponentialVariables
8.3StochasticCalculusofVariationsforPoissonProcesses
……
AVolatilityEstimationbyFourierExpansion
BStrongMonte-CarloApproximation
CNumericalImplementation
References
Index