简介：In recent years products based on financial derivatives have become an indispensable
tool for risk managers and investors. Insurance products have become
part of almost every personal and business portfolio. The management of mutual
and pension funds has gained in importance for most individuals. Banks,
insurance companies and other corporations are increasingly using financial
and insurance instruments for the active management of risk. An increasing
range of securities allows risks to be hedged in a way that can be closely tailored
to the specific needs of particular investors and companies. The ability
to handle efficiently and exploit successfully the opportunities arising from
modern quantitative methods is now a key factor that differentiates market
participants in both the finance and insurance fields. For these reasons it is
important that financial institutions, insurance companies and corporations
develop expertise in the area of quantitative finance, where many of the associated
quantitative methods and technologies emerge.
BasicNotation ............................................XIII
1PreliminariesfromProbabilityTheory.....................1
1.1DiscreteRandomVariablesandDistributions...............1
1.2ContinuousRandomVariablesandDistributions............11
1.3MomentsofRandomVariables............................22
1.4JointDistributionsandRandomVectors...................39
1.5Copulas(*).............................................50
1.6ExercisesforChapter1..................................53
2StatisticalMethods ........................................55
2.1LimitTheorems.........................................55
2.2Con?denceIntervals.....................................63
2.3EstimationMethods.....................................70
2.4MaximumLikelihoodEstimation..........................78
2.5NormalVarianceMixtureModels..........................81
2.6DistributionofIndexLog-Returns.........................84
2.7ConvergenceofRandomSequences........................92
2.8ExercisesforChapter2..................................98
3ModelingviaStochasticProcesses .........................99
3.1IntroductiontoStochasticProcesses.......................99
3.2CertainClassesofStochasticProcesses.....................106
3.3DiscreteTimeMarkovChains.............................110
3.4ContinuousTimeMarkovChains..........................113
3.5PoissonProcesses........................................120
3.6LevyProcesses(*).......................................126
3.7InsuranceRiskModeling(*)..............................128
3.8ExercisesforChapter3..................................131
4DiusionProcesses ........................................133
4.1ContinuousMarkovProcesses .............................133
4.2ExamplesforContinuousMarkovProcesses.................136
4.3Di?usionProcesses ......................................141
4.4KolmogorovEquations..................................145
4.5Di?usionswithStationaryDensities.......................154
4.6Multi-DimensionalDi?usionProcesses(*)..................159
4.7ExercisesforChapter4..................................161
5MartingalesandStochasticIntegrals.......................163
5.1Martingales.............................................163
5.2QuadraticVariationandCovariation.......................174
5.3GainsfromTradeasStochasticIntegral....................187
5.4It?oIntegralforWienerProcesses..........................193
5.5StochasticIntegralsforSemimartingales(*).................197
5.6ExercisesforChapter5..................................203
6TheItoFormula ...........................................205
6.1TheStochasticChainRule...............................205
6.2MultivariateIt?oFormula.................................209
6.3SomeApplicationsoftheIt?oFormula......................213
6.4ExtensionsoftheIt?oFormula.............................222
6.5LevyˉsTheorem(*......................................227
6.6AProofoftheIt?oFormula(*)............................230
6.7ExercisesforChapter6..................................234
7StochasticDierentialEquations ..........................237
7.1SolutionofaStochasticDi?erentialEquation...............237
7.2LinearSDEwithAdditiveNoise...........................241
7.3LinearSDEwithMultiplicativeNoise......................243
7.4VectorStochasticDi?erentialEquations....................246
7.5ConstructingExplicitSolutionsofSDEs....................248
7.6JumpDi?usions(*)......................................254
7.7ExistenceandUniqueness(*).............................261
7.8MarkovianSolutionsofSDEs(*)..........................272
7.9ExercisesforChapter7..................................275
8IntroductiontoOptionPricing ............................277
8.1Options................................................277
8.2OptionsundertheBlack-ScholesModel....................281
8.3TheBlack-ScholesFormula...............................288
8.4SensitivitiesforEuropeanCallOption.....................290
8.5EuropeanPutOption....................................295
8.6HedgeSimulation........................................298
8.7SquaredBesselProcesses(*) ..............................304
ContentsXI
8.8ExercisesforChapter8..................................317
9VariousApproachestoAssetPricing ......................319
9.1RealWorldPricing......................................319
9.2ActuarialPricing........................................329
9.3CapitalAssetPricingModel..............................332
9.4RiskNeutralPricing.....................................336
9.5GirsanovTransformationandBayesRule(*)................345
9.6ChangeofNumeraire(*).................................350
9.7Feynman-KacFormula(*)................................356
9.8ExercisesforChapter9..................................364
10ContinuousFinancialMarkets .............................367
10.1PrimarySecurityAccountsandPortfolios..................367
10.2GrowthOptimalPortfolio................................372
10.3SupermartingaleProperty................................375
10.4RealWorldPricing......................................378
10.5GOPasBestPerformingPortfolio.........................386
10.6Diversi?edPortfoliosinCFMs............................389
10.7ExercisesforChapter10.................................402
11PortfolioOptimization.....................................403
11.1LocallyOptimalPortfolios................................404
11.2MarketPortfolioandGOP...............................415
11.3ExpectedUtilityMaximization............................419
11.4PricingNonreplicablePayo?s.............................427
11.5Hedging...............................................430
11.6ExercisesforChapter11.................................437
12ModelingStochasticVolatility .............................439
12.1StochasticVolatility.....................................439
12.2Modi?edCEVModel....................................444
12.3LocalVolatilityModels...................................461
12.4StochasticVolatilityModels..............................472
12.5ExercisesforChapter12.................................481
13MinimalMarketModel ....................................483
13.1ParametrizationviaVolatilityorDrift.....................483
13.2StylizedMinimalMarketModel...........................488
13.3DerivativesundertheMMM..............................496
13.4MMMwithRandomScaling(*)...........................503
13.5ExercisesforChapter13.................................511
14MarketswithEventRisk ..................................513
14.1JumpDi?usionMarkets..................................513
14.2Diversi?edPortfolios.....................................523
14.3Mean-VariancePortfolioOptimization.....................532
14.4RealWorldPricingforTwoMarketModels.................536
14.5ExercisesforChapter14.................................549
15NumericalMethods........................................551
15.1RandomNumberGeneration..............................551
15.2ScenarioSimulation......................................558
15.3ClassicalMonteCarloMethod............................570
15.4MonteCarloSimulationforSDEs.........................578
15.5VarianceReductionofFunctionalsofSDEs.................587
15.6TreeMethods...........................................591
15.7FiniteDi?erenceMethods................................600
15.8ExercisesforChapter15.................................611
16SolutionsforExercises.....................................615
Acknowledgements ........................................667
References.....................................................669
AuthorIndex..................................................685
Index ..........................................................691
[/UseMoney]
MathematicsSubjectClassication(2000):62P05,60G35,62P20
JELClassication:G10,G13
LibraryofCongressControlNumber:2006932290
ISBN-103-540-26212-1 SpringerBerlinHeidelbergNewYork
ISBN-13978-3-540-26212-1 SpringerBerlinHeidelbergNewYork
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