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Publié par | universitat_duisburg-essen |
Publié le | 01 janvier 2011 |
Nombre de lectures | 63 |
Poids de l'ouvrage | 1 Mo |
Extrait
STRUCTUREDLIFEINSURANCEAND
INVESTMENTPRODUCTSFORRETAIL
INVESTORS
VONDERMERCATORSCHOOLOFMANAGEMENT
-FAKULTA¨TFU¨RBETRIEBSWIRTSCHAFTSLEHRE-DERUNIVERSITA¨T
DUISBURG-ESSEN
ZURERLANGUNGDESAKADEMISCHENGRADES
EINESDOKTORSDERWIRTSCHAFTSWISSENSCHAFTEN(DR.RER.OEC.)
GENEHMIGTEDISSERTATION
NOVJUDITHCHRISTIANESCHNEIDER
AUSBONN
REFERENT:PROF.DR.ANTJEMAHAYNI
KORREFERENT:PROF.DR.JOACHIMPRINZ
TAGDERMU¨NDLICHENPRU¨FUNG:15.03.2011
wledgementsAckno
Ftor/leaderoremost,IforthankmymyacademicsupervisorstudiesProf.givingDr.meAntjevariousMahayniassistance,whowasnotsuggestionsonlyaandmen-ad-
vice,whichbutsupportsProf.Dref.fectiAntjeve,efMahaynificientalsoandcreatesdelightfulafantasticresearching.atmosphereWithoutinherthismydepartmentPhD
couldnothaverunsosmoothly.Moreover,Ihadthehonortobeaco-authorandto
profitfromProf.Dr.AntjeMahayniscreativeideas,excellenceandexperience.Ihave
toexpressmydeepestgratitude!
aneLikexcellentwise,Ithankco-authorinanotherher,Ico-authoralsohadProf.theDr.opportunityNicoletoBrangergain.fromBesidesherhaknovingwledgesuch
duringdoctoraltheseminars.SummerHerSchoolenthusiasm2008inandNaurodpassionandinourvresearchariousareeotherxceptionalmeetings.Thankduringyou!the
tothankMoreoinver,particularamongstProf.theDr.peopleAnnettewhogKa¨veohlerme,vProf.aluableDr.JoachimsupportsPriandnz,Prof.comments,Dr.IKlauslike
neckiSandmannand-themycolleaguesDiplomaandsupervisorfriends-,fromProf.theDr.UniJensvSersity¨udekum,ofBonnDr.andMichaeltheLogisticSucha-
Dr.SvDepartmentenBalderof,theUniSusanneversityBrand,ofDuisbSarahurBrand,g-Essen.DanielSpecialSteuten,thanksgoDanieltomySchwake,colleaguesTim
whoPetershavandealsoDanielbecomeZielingfriends.fromtheDepartmentofInsuranceandRiskManagement
supportLastbutduringnotmyleast,Ieducationwishtoandtfarhankbemyyond.fYamilyou,areinallparticulardeartomymyheart!mother,fortheir
v
Contents
1IntroductionandMotivation.......................................
PartIStructuredLifeInsuranceProducts
2StructuredLifeInsuranceProducts:ASurvey.......................
2.1Introduction...................................................
2.1.1Fromclassicallifeinsurancetostructuredlifeinsuranceproducts
2.1.2Characteristicsofstructuredlifeinsuranceproducts............
2.2Classificationoftherelevantliterature.............................
2.2.1Modelchoice............................................
2.2.2Riskmanagement........................................
2.2.3Additionalridersandtheirpricingandriskmanagement........
2.3Interactionbetweeninsurancecompanyandinsured.................
2.4Conclusion...................................................
3OptimalDesignofInsuranceContractswithGuarantees..............
3.1Introduction...................................................
3.2Productdesign................................................
3.3Financialmarketandinvestmentstrategies.........................
3.3.1Completefinancialmarketmodel...........................
3.3.2Investmentstrategies......................................
3.3.3Pricingoftheembeddedoptions............................
3.3.4Analysisandillustrationoffairinsurancepayoffs..............
3.4Optimalinsurancecontractandbenchmarkutility...................
3.4.1Utilityloss..............................................
3.4.2Comparisonoftheutilitylosses.............................
3.5Conclusion...................................................
4VariableAnnuitiesandtheOptiontoseekrisk:Whyshouldyou
diversify?........................................................
4.1Introduction...................................................
4.2Contractspecification,modelsetupandpricing.....................
4.3Optimalchoiceofinvestmentstrategyunderbackgroundrisk.........
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viii
Contentsviii4.3.1Comparisonofputprices..................................64
4.3.2Backgroundrisk,generalizedconstantmixstrategiesand
optimality...............................................66
4.3.3Borrowingconstraints.....................................70
4.4NumericalIllustration..........................................71
4.4.1Comparisonofputprices..................................72
4.4.2Utilityloss..............................................74
4.4.3Realisticexample.........................................77
4.5Conclusion...................................................79
PartIIStructuredInvestmentProducts
5PricingandUpperPriceBoundsofRelaxCertificates.................83
5.1Introduction...................................................83
5.2Productspecification...........................................87
5.2.1Productspecification......................................87
5.2.2Attractiverelaxcertificates.................................88
5.3Risk-neutralpricingandupperpricebounds........................90
5.3.1Risk-neutralpricingofrelaxcertificates......................90
5.3.2Upperpriceboundsbasedoncouponbonds...................92
5.3.3Upperpriceboundsbasedonsmallerrelaxcertificates........94
5.4Numericalexamples............................................97
5.4.1Risk-neutralmeasure......................................97
5.4.2Pricesofrelaxcertificates..................................98
5.5Marketcomparison............................................107
5.5.1Contractspecifications....................................107
5.5.2Survivalprobabilitiesandpricebounds......................107
5.6Conclusion...................................................110
6Sub-optimalinvestmentstrategiesandmispricedputoptionsunder
borrowingconstraints.............................................113
6.1Introduction...................................................113
6.2Optimalportfolioselectionwithterminalwealthguaranteeand
borrowingconstraints...........................................115
6.2.1CRRAUtility............................................117
6.2.2HARAUtility............................................121
6.3Utilityloss....................................................125
6.3.1Utilitylosscausedbytheguaranteeandborrowingconstraints...127
6.3.2UtilitylosscausedbyCPPI................................128
6.3.3Mispricedputoptionsvs.suboptimalinvestmentstrategies......129
6.4Conclusion...................................................130
7ConclusionandFutureResearch...................................133
Contents
ix
AAppendix........................................................137
A.1AppendixChapter4............................................137
A.1.1ProofofTheorem4.1.....................................137
A.1.2ProofofProposition4.2...................................138
A.1.3ProofofProposition4.3...................................139
A.1.4ProofofProposition4.4...................................140
A.2AppendixChapter5............................................141
A.2.1FirstHittingTime-One-DimensionalCase...................141
A.2.2FirstHittingTime–TwoDimensionalCase..................143
A.3AppendixChapter6............................................146
A.3.1ProofofProposition6.1...................................146
Bibliography.........................................................147
References........................................................147
ablesTofList
2.12.22.32.42.5
3.13.2
4.14.24.3
5.15.2
6.16.2
Productfeatures...............................................12
Modelchoice.................................................17
Problemsinriskmanagement....................................19
Riskmanagement..............................................22
Additionalriders...............................................26
Investmentstrategies...........................................39
Lossratesandoptimalinvestmentfractions........................51
Benchmarkmodelandcontractparameters.........................61
IncomeandPensionParameters..................................78
TheTablegivesthelossratesofthelow,mediumandhigh
GMAB-investorforvaryingriskaversionlevelsγinbasispoints.The
parametersaresetasstatedinTable4.1and6.1.....................79
Summaryoftradedproductspecificationsandinterestrates...........108
Priceboundsfortradedcertificates...............................109
Benchmarksetupandstrategyparameters..........................121
Riskaversionvs.impliedriskaversion............................126
xi
ListesFigurof
3.13.23.33.43.54.14.24.34.4
5.15.25.35.45.56.1
Payoffofguaranteeschemes....................................36
Fairparticipationratesαforπ=1...............................44
Fairparticipationratesαforbuyandholdandconstantmixstrategies..45
Lossrateforconstantmixstrategy................................49
Lossratesforbuy-and-holdandCPPI.............................50
Fairversusfeasibleinvestmentfractions..........................62
Fair(solidline)andfeasible(dashedline)putpricesaspercentageof
theworstcasepriceforvaryinglevelsofriskaversionγ.Inbothplots,
thetimetomaturityisT=10.Theotherparametersaregivenasin
Table4.1.....................................................72
Fair(solidline)andfeasible(dashedline)putpricesaspercentage
oftheworstcasepriceforvaryingmeanofthebackgroundrisk.The
timetomaturityisT=10andtheriskaversionissettoγ=2.The
otherparametersaregivenasinTable4.1..........................74
ri