Mathematical and Statistical Methods for Actuarial Sciences and Finance

401 Pages·2012·6.09 MB·English

by  Giuseppina Albano

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MathematicalandStatisticalMethodsforActuarialSciencesandFinance
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CiraPerna(Editor)
MarilenaSibillo(Editor) I
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Mathematical and
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Statistical Methods U
for Actuarial Sciences
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and Finance
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Editors
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CiraPerna
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DepartmentofEconomicsandStatistics
UniversityofSalerno
[email protected] C
MarilenaSibillo
DepartmentofEconomicsandStatistics S
UniversityofSalerno
[email protected]
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The publication of this book has been made possible thanks to thMe financial support of the
UniversitàdegliStudidiSalerno.
ISBN978-88-470-2341-3 e-ISBN978-88-470-2342-0
DOI10.1007/978-88-470-2342-0

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LibraryofCongressControlNumber:2011932217
SpringerDordrechtHeidelbergLondonMilanNewYorkE
©Springer-VerlagItalia,2012
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notimply,even intheabsence of aspecificstatement,thatsuchnames areexemptfromthe
relevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
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Springer-VerlagItaliasrl–ViaDecembrio28–20137Milano
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Preface
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TheMAF2010Conference,organizedbyUniversityofSalernoinRavello(Salerno,
Italy),wasdevelopedonthebasisofcooperationbetweenmathemAaticiansandstatis-
ticiansworkingininsuranceandfinancefields.
The idea arises from the belief that the interdisciplinary approach can improve
research on these topics, and the proof of this is that intereMst in this guideline has
evolvedandbeenre-enforced.
TheConferenceaimsatprovidingstateoftheartresearchindevelopment, im-
plementationandrealworldapplicationsofstatisticalandmathematicalmodelsin

actuarialandfinancesciences,aswellasfordiscussionofproblemsofnationaland

internationalinterest. D
Theseconsiderationsimplythestrengtheningoftheinvolvedmethodsandtech-
niquestowardsthepurpose,sharedbyanincreasingpartofthescientificcommunity,
oftheintegration betweenmathematics andstatEistics appliedinfinanceandinsur-
ancefields.
TheConferencewasopentobothacademicandnon-academiccommunitiesfrom
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universities,insurancecompaniesandbanks,anditwasspecificallydesignedtocon-
tribute in fostering the cooperation between practitioners and theoreticians in the
field. S
About170researchersattendedtheConferenceandatotalof25contributedses-
sions and 9 organized sessions, contaIining more than 130 communications, were
acceptedforthepresentation.
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Fourprestigiouskeynotelecturersincreasedthescientificvalueofthemeeting:
• NonparametricmethodsinsurvBivalanalysisbyProf.NarayanaswamyBalakrish-
nan(McMasterUniversity,Canada)
• SomeRecentDevelopments inMultiplicative ErrorModels byProf.Giampiero
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Gallo(UniversityofFlorence,Italy)
• TooInterconnectedtoFail:FinancialContagionandSystemicRiskinNetwork
ModelofCreditDefaultSwapsandCreditEnhancementObligationsofUSBanks
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byProf.SheriMarkose(UniversityofEssex,U.K.)
• SomeResultsforSkip-FreeRandomWalksbyProf.SheldonM.Ross(University
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ofCalifornia,Berkeley,U.S.A.).
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Thecollectionpublishedheregatherssomeofthepaperspresentedattheconference
MAF2010 and successively worked out to this aim. They cover a wide variety ofI
subjects:
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MathematicalModelsforInsurance:InsurancePortfolioRiskAnalysis,Solvency,
Longevity Risk, Actuarial models, Management in Insurance Business, Stochastic
modelsinInsurance. C
StatisticalMethodsforFinance:AnalysisofHighFrequencyData,DataMining,
Nonparametric methods for the analysis of financial time series, Forecasting from
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DynamicPhenomena,ArtificialNeuralNetwork,MultivariateMethodsfortheAnal-
ysisofFinancialMarkets.
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MathematicalToolsinFinance:StockmarketRiskandSelection,Mathematical
ModelsforDerivatives,StochasticModelsforFinance,StochasticOptimization.
Thepapersfollowinalphabeticorderfromthefirstauthor. N
The scientific value of the papers is due to the authors and, in the name of the
scientific and organizing committee of the conference MAF2010, we truly thank
themall.InparticularwewanttopointoutthepreciouscooperaAtionofthereferees:
theirworkhasbeendecisiveintheimprovementofthequalityofthisbook.
MoreoverwethanktheFacultyofEconomics,theFacultyofPoliticalSciences
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andtheDepartmentofEconomicsandStatisticsoftheUniversityofSalernoforthe
opportunitytheygaveustogoaheadwiththisidea.
WewouldliketoexpressourgratitudetothemembersoftheScientificandOrga-
nizingCommitteeandtoallthepeoplewhocontributed tothesuccessoftheevent.
Wearegratefulforthekindeffortinparticularof thesponsors:ItalianAssocia-
tionforMathematicsappliedtoEconomicsandSociaDlSciences(AMASES),Italian
Statistical Society (SIS), Comune di Fisciano, Comune di Mercato San Severino,
ComunediRavello, Assessoratoalle Politiche Ambientali ofProvinciadiSalerno
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formakingthemeetingmorecomfortableandpleasant.Wewouldlikeaswelltoex-
pressspecialacknowledgementstoSpringerEditor,foritssupportintheinitiative.
Finally,wetrulythanktheDepartmentofHAppliedMathematicsandtheDepart-
ment of Statistics of the University of Venice for the enthusiastic sharing and the
cooperationinthisinitiativeandfortheinvolvementinorganizingandhostingthe
nexteditionoftheConference,tobeheldSin2012inVenice.
Fisciano,May2011 I CiraPernaandMarilenaSibillo
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ScientificCommittee
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ChrisAdcock,UniversityofSheffield(UK)
AlessandraAmendola,UniversityofSalerno(IT) R
AnnaRitaBacinello,UniversityofTrieste(IT)
GiovanniBaroneAdesi,UniversityofLugano(CH)
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AntonellaBasso,UniversityCa’FoscariofVenice(IT)
MarcoCorazza,UniversityCa’FoscariofVenice(IT)
EmiliaDiLorenzo,UniversityofNaplesFedericoII(IT) S
ElsaFornero,UniversityofTurin(IT)
StevenHaberman,CityUniversityLondon(UK) U
MicheleLaRocca,UniversityofSalerno(IT)
NicolaLoperfido,UniversityofUrbino(IT)
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EliseoNavarro,UniversityofCastilla-LaMancha(ES)
AnnamariaOlivieri,UniversityofParma(IT)
ErmannoPitacco,UniversityofTrieste(IT)
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ClaudioPizzi,UniversityCa’FoscariofVenice(IT)
IsabellaProcidano,UniversityCa’FoscariofVenice(IT)
CosimoDamianoVitale,UniversityofSalerno(IT) M
OrganizingCommittee
GiuseppinaAlbano,UniversityofSalerno(IT)
DianaBarro,UniversityCa’FoscariofVenice(IT)
GiovannaBimonte,UniversityofSalerno(IT) D
PietroCoretto,UniversityofSalerno(IT)
ValeriaD’Amato,UniversityofSalerno(IT)
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FrancescoGiordano,UniversityofSalerno(IT)
MartinaNardon,UniversityCa’FoscariofVenice(IT)
MarcellaNiglio,UniversityofSalerno(IT) H
MariaLuciaParrella,UniversityofSalerno(IT)
MarialuisaRestaino,UniversityofSalerno(IT)
MariaRussolillo,UniversityofSalerno(IST)
GiuseppeStorti,UniversityofSalerno(IT)
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Contents
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OntheestimationincontinuouslimitofGARCHprocesses
GiuseppinaAlbano,FrancescoGiordano,andCiraPerna ...A............ 1
Variableselectioninforecastingmodelsfordefaultrisk
AlessandraAmendola,MarialuisaRestaino,andLucaSensiMni ............ 11
Capitalstructurewithfirm’snetcashpayouts
FlaviaBarsotti,MariaElviraMancino,andMoniquePontier............. 19

Convex ordering of Esscher and minimal entropy martingale measures
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fordiscretetimemodels
FabioBelliniandCarloSgarra ..................................... 27
OnhyperboliciterateddistortionsfortheadjuEstmentofsurvival
functions
AlexisBienvenu¨eandDidierRullie`re ......H.......................... 35
BeyondBasel2:Modelinglossgivendefaultthroughsurvivalanalysis
StefanoBoniniandGiulianaCaivano ...S............................. 43
Initial premium, aggregate claims and distortion risk measures in XL
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reinsurancewithreinstatements
AntonellaCampanaandPaolaFerreLtti............................... 53
Population dynamics in a spatial Solow model with a convex-concave
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productionfunction
VincenzoCapasso,RalfEngbers,andDavideLaTorre .................. 61
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PopulationdynamicsinapatchgrowthmodelwithS-shapedproduction
functionsandmigrationeffects
VincenzoCapasso,HerbEP.Kunze,andDavideLaTorre................. 69
Anordinalapproachtoriskmeasurement
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MartaCardinandMiguelCouceiro.................................. 79
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Piecewiselineardynamicsystemsforownrisksolvencyassessment
RoccoRobertoCerchiaraandFabioLamantia......................... 87I
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Valuationoftheconditionalindexationoptioninassetandliability
managementofdefinedbenefitpensionfunds
RosaCocozza,AngelaGallo,andGiuseppeXella.......................C95
Conditionalperformanceattributionforequityportfolio
ClaudioConversanoandAlessioLizzeri ...........................S... 105
Capital requirements for aggregate risks in long term living products:
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Astochasticapproach
MariarosariaCoppola,AlbinaOrlando,andMassimilianoPolitano........ 115
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Portfolio selection with an alternative measure of risk: Computational
performancesofparticleswarmoptimizationandgeneticalgorithms
MarcoCorazza,GiovanniFasano,andRiccardoGusso ................. 123
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Interdependenceandcontagionininternationalstockmarkets:Alatent
Markovmodelapproach
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MicheleCosta,LucaDeAngelis,andLeonardJ.Paas................... 131
Valuationofportfoliolossderivativesinaninfectiousmodel
AreskiCousin,DianaDorobantu,andDidierRullie`re ................... 139

Internalriskcontrolbysolvencymeasures
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ValeriaD’Amato,EmiliaDiLorenzo,MariaRussolillo,andMarilenaSibillo 149
Measuringmortalityheterogeneityinpensionannuities
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ValeriaD’Amato,GabriellaPiscopo,andMariaRussolillo............... 157
IstechnicalanalysisabletobeatmarketinHefficiency?
ElisaDaniotti ................................................... 165
Onthedampedgeometrictelegrapher’Ssprocess
AntonioDiCrescenzo,BarbaraMartinucci,andShelemyahuZacks ........ 175
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RiskmeasuresandParetostyletails
AnnaMariaFiori,EmanuelaRosazzLaGianin,andAnnaSpasova.......... 183
Creditriskandincompleteinformation:Afilteringframework
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forpricingandriskmanagement
ClaudioFontana................................................. 193
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Claimsreservinguncertaintyinthedevelopmentofinternal
riskmodels
SalvatoreForte,MatteoIaPlenti,andMarcoPirra....................... 203
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Contents XI
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Someinequalitiesbetweenmeasuresofmultivariatekurtosis,
withapplicationtofinancialreturns I
CinziaFranceschiniandNicolaLoperfido ............................ 211
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Thegeneralizedtrapezoidalmodelinfinancialdataanalysis
ManuelFranco,JohanRene´ vanDorp,andJuana-Mar´ıaVivo ............C219
Nonparametricestimationofvolatilityfunctions:Someexperimental
evidences S
FrancescoGiordano,MicheleLaRocca,andCiraPerna ................ 229
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Investigating and modelling the perception of economic security in the
SurveyofHouseholdIncomeandWealth
MariaIannarioandDomenicoPiccolo ......................N......... 237
Onruinprobabilitiesinriskmodelswithinterestrate
NinoKordzakhia,AlexanderNovikov,andGuramiTsitsiashviliA........... 245
Onlongevityrisksecuritizationandsolvencycapitalrequirementsinlife
annuities M
SusannaLevantesi,MassimilianoMenzietti,andTizianaTorri ............ 255
Modellingthesharepricesasahiddenrandomwalkonthelamplighter

group
XiaojuanMaandSergeyUtev .................. .................... 263
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Multivariatejumparrivals:Thevariancegammacase
RobertoMarfe`................................................... 271
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Modellingtheskewedexponentialpowerdistributioninfinance
J.MiguelMar´ınandGenaroSucarrat......H.......................... 279
Compositeindicators:Asectorialperspective
MarcoMarozzi .....................S............................. 287
Dynamicmodelofpensionsavingsmanagementwithstochasticinterest
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ratesandstockreturns
IgorMelichercˇ´ıkandDaniel SˇevcˇoviLcˇ................................ 295
Financialanddemographicrisksimpactonapay-as-you-go
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pensionfund
RobertaMelisandAlessandroTrudda................................ 305
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Extractingimplied dividendsfrom optionsprices: Someapplicationsto
theItalianderivativesmarket
MartinaNardonandPaolPoPianca .................................. 315
Generalizationofsomelineartimeseriespropertytononlineardomain
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MarcellaNiglioandCosimoDamianoVitale .......................... 323
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Evaluatingthebehaviorofafunctioninkernelbasedregression
MariaLuciaParrella ............................................. 333I
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Optimaltradingrulesathourlyfrequencyintheforeignexchange
markets
DaniloPelusiandMassimoTivegna .................................C341
The influence of correlation and loading on M-V efficient retentions in
variablequotashareproportionalreinsurance S
FlavioPressaccoandLauraZiani................................... 349
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Goodandbadbanks
LucaRegis...................................................... 359
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Taildiversificationstrategy.AnapplicationtoMSCIWorldSector
Indices
GiorgiaRivieccio................................................ 367
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Marginalizationandaggregationofexponentialsmoothingmodels
inforecastingportfoliovolatility
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GiacomoSbranaandAndreaSilvestrini .............................. 375
GeneralizationofstratifiedvariancereductionmethodsforMonteCarlo
exchangeoptionspricing
GiovanniVillani ............................. .................... 383
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Pricediscoveryinadynamicstructuralmodel
LeiWuandHansvanderWeide .................................... 393
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SubjectIndex ......................................................403
AuthorIndex ..........................H............................407
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