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Investment guarantees PDF

358 Pages·2003·3.17 MB·English
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Investment Guarantees Modeling and Risk Management for Equity-Linked Life Insurance MARY HARDY John Wiley & Sons, Inc. Investment Guarantees Founded in 1807, John Wiley & Sons is the oldest independent publishing companyintheUnitedStates.WithofficesinNorthAmerica,Europe,Aus- tralia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional andpersonalknowledgeandunderstanding. TheWileyFinanceseriescontainsbookswrittenspecificallyforfinanceand investment professionals as well as sophisticated individual investors and their financial advisors. Book topics range from portfolio management to e-commerce,riskmanagement,financialengineering,valuationandfinancial instrumentanalysis,aswellasmuchmore. Foralistofavailabletitles,visitourWebsiteatwww.WileyFinance.com. Investment Guarantees Modeling and Risk Management for Equity-Linked Life Insurance MARY HARDY John Wiley & Sons, Inc. Thisbookisprintedonacid-freepaper.(cid:1)(cid:1) Copyright(cid:1)2003byMaryHardy.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted inanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanning,or otherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyright Act,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthrough paymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222 RosewoodDrive,Danvers,MA01928,978-750-8400,fax978-750-4470,oronthewebat www.copyright.com.RequeststothePublisherforpermissionshouldbeaddressedtothe PermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030, 201-748-6011,fax201-748-6008,e-mail:permcoordinator(cid:2)wiley.com. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheir besteffortsinpreparingthisbook,theymakenorepresentationsorwarrantieswithrespect totheaccuracyorcompletenessofthecontentsofthisbookandspecificallydisclaimany impliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.Nowarrantymay becreatedorextendedbysalesrepresentativesorwrittensalesmaterials.Theadviceand strategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsultwitha professionalwhereappropriate.Neitherthepublishernorauthorshallbeliableforanyloss ofprofitoranyothercommercialdamages,includingbutnotlimitedtospecial,incidental, consequential,orotherdamages. Forgeneralinformationonourotherproductsandservices,ortechnicalsupport,please contactourCustomerCareDepartmentwithintheUnitedStatesat800-762-2974,outside theUnitedStatesat317-572-3993orfax317-572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsin printmaynotbeavailableinelectronicbooks. FormoreinformationaboutWileyproducts,visitourwebsiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationData: Hardy,Mary,1958- Investmentguarantees:modelingandriskmanagementforequity-linkedlifeinsurance/ MaryHardy. p.cm.–(Wileyfinanceseries) Includesbibliographicalreferencesandindex. ISBN0-471-39290-1(cloth:alk.paper) 1.Insurance,Life-mathematicalmodels.2.Riskmanagement–Mathematicalmodels. 1.title.II.Series. HG8781.H3132003 368.32’0068’1–dc21 2002034200 PrintedintheUnitedStatesofAmerica. 10987654321 Acknowledgments T his work has been supported by the National Science and Engineering Research Council of Canada, and by the Actuarial Education and Research Fund. I would also like to thank the members of the Department of Statistics at the London School of Economics and Political Science for their hospitality while the book was being completed, especially Anthony Atkinson,AngelosDassios,MartinKnott,andRagnarNorberg. IwouldliketothankTaylorandFrancis,publishersoftheScandinavian ActuarialJournal,forpermissiontoreproducematerialfromBayesianRisk ManagementforEquity-LinkedInsuranceinChapter5. I learned a great deal from my fellow members of the magnificent CanadianInstituteofActuariesTaskForceonSegregatedFunds.Inpartic- ular,IwouldliketothankGeoffreyHancock,whohasprovidedinvaluable advice and assistance during the preparation of this book. Also, thanks to Martin Le Roux, David Gilliland, and the two Chairs, Simon Curtis and MurrayTaylor,whohadalottoputupwith,notleastfromme. Ihavebeenveryluckytoworkwithsomewonderfulcolleaguesandstu- dentsovertheyears,manyofwhomhavecontributeddirectlyorindirectly to this book. In particular, thanks to Andrew Cairns, Julia Wirch, David Wilkie,JudithChan,KarenChau,GeoffThiessen,YuanTao,So-YuenKim, AnpingWang,BoyangLiu,HarryPanjer,andSheauwenYang.Thanksalso to Glen Harris, who introduced me to regime-switching models. It is a special privilege to work with Ken Seng Tan at the University of Waterloo andwithHowardWatersatHeriot-WattUniversity. Mybrother,PeterHardy,workedwithmetopreparetheRSLNsoftware (HardyandHardy2002),whichisausefulcomplementtothiswork.Itwas goodfunworkingwithhim. Mostly I would like to express my deepest gratitude to my husband, Phelim Boyle, for his unstinting encouragement, support, and patience; culinary contributions; and unwavering readiness to share with me his encyclopedicknowledgeoffinance. M.H. v Contents Introduction xi CHAPTER 1 Investment Guarantees 1 Introduction 1 MajorBenefitTypes 4 ContractTypes 5 Equity-LinkedInsuranceandOptions 7 ProvisionforEquity-LinkedLiabilities 11 PricingandCapitalRequirements 14 CHAPTER 2 Modeling Long-Term Stock Returns 15 Introduction 15 DeterministicorStochastic? 15 EconomicalTheoryorStatisticalMethod? 17 TheData 18 TheLognormalModel 24 AutoregressiveModels 27 ARCH(1) 28 Regime-SwitchingLognormalModel(RSLN) 30 TheEmpiricalModel 36 TheStableDistributionFamily 37 GeneralStochasticVolatilityModels 38 TheWilkieModel 39 VectorAutoregression 45 CHAPTER 3 Maximum Likelihood Estimation for Stock Return Models 47 Introduction 47 PropertiesofMaximumLikelihoodEstimators 49 SomeLimitationsofMaximumLikelihoodEstimation 52 vii

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Praise for InvestmentGuarantees "In addition to being a valuable and innovative addition to the literature on risk management of equity-linked insurance, this book provides a uniquely clear demonstration of using different measures in a very practical context. A great way of showing actuaries how to
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