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Contents
1.1Introduction............................. 9
1.2 Π-stabledistributions........................ 10
1.2.1Characteristicfunctionrepresentation.......... 10
1.2.2Computing Π-stabledistributions............. 15
1.2.3Simulationof Π-stablevariables.............. 16
1.2.4Tailbehavior........................ 17
1.3Estimationofparameters..................... 19
1.3.1Tailexponentestimation................. 19
1.3.2SampleQuantilesMethods................ 20
1.3.3SampleCharacteristicFunctionMethods........ 23
1.4Financialapplicationsof Π-stablelaws.............. 26
2Taildependence33
RafaelSchmidt
2.1Taildependenceandcopulae................... 33
2.2Calculatingthetail-dependencecoe?cient............ 36
2.2.1Archimedeancopulae................... 36
2.2.2Ellipticallycontoureddistributions............ 37
2.2.3Othercopulae........................ 40
2.3Estimatingthetail-dependencecoe?cient............ 43
2.4Estimationandempiricalresults................. 45
Bibliography............................... 53
FuzzyIdenti?cationModel55
oerAzamAchsani, HizirSofyan
3.1Introduction............................. 55
3.2MoneyDemand........................... 57
3.3Takagi-SugenoApproach...................... 58
3.4FuzzyC-Means........................... 59
3.5ModelIdenti?cation........................ 60
3.6CaseStudy:IndonesianMoneyDemand............. 61
3.7Conclusions............................. 63
Bibliography............................... 65
ImpliedTrinomialTrees67
arelKomorΓa
4.1Introduction............................. 67
4.2BasicOptionPricingOverview.................. 69
4.3TreesandImpliedModels..................... 71
4.4ITTΓfisandTheirConstruction.................. 74
4.4.1Basicinsight........................ 74
4.4.2Statespace......................... 76
4.4.3Transitionprobabilities.................. 78
4.4.4Possiblepitfalls....................... 79
4.4.5Illustrativeexamples.................... 80
.5ComputingImpliedTrinomialTrees............... 86
4.5.1Basicskills......................... 86
4.5.2Advancedfeatures..................... 93
4.5.3Whatishidden....................... 96
ibliography............................... 99
.1Introduction............................. 101
.2NonparametricHullMethods................... 103
5.2.1AnOverview........................ 103
5.2.2DataEnvelopmentAnalysis................ 104
5.2.3FreeDisposalHull..................... 104
.3DEAinPractice:InsuranceAgencies.............. 105
.4FDHinPractice:ManufacturingIndustry........... 106
.1Introduction............................. 113
.2ComputationtheexacttestsintheXploRe........... 115
.3Illustrativeexamples........................ 116
6.3.1Timeprocessingestimation................ 116
6.3.2Estimationwithmissingtime-to-failureinformation.. 120
6.4ImplementationtotheXploRe.................. 126
6.5Asymptoticaloptimality...................... 126
6.6Informationandexacttestinginthegammafamily....... 127
6.7TheLambertWfunction..................... 129
6.8Oversizingoftheasymptotics................... 129
Bibliography............................... 133
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