Actuarial and Financial Risks: Models, Statistical Inference, and Case Studies

298 Pages·2010·14.39 MB·English

Journal of Probability and Statistics
Actuarial and Financial Risks: Models,
Statistical Inference, and Case Studies
Guest Editors: Ričardas Zitikis, Edward Furman, Abdelhakim Necir,
Johanna Nešlehová, and Madan L. Puri
Actuarial and Financial Risks: Models,
Statistical Inference, and Case Studies
Journal of Probability and Statistics
Actuarial and Financial Risks: Models,
Statistical Inference, and Case Studies
Guest Editors: Ricˇardas Zitikis, Edward Furman, Abdelhakim Necir,
Johanna Nesˇlehova´, and Madan L. Puri
Copyrightq 2010HindawiPublishingCorporation.Allrightsreserved.
Thisisanissuepublishedinvolume2010of“JournalofProbabilityandStatistics.”Allarticlesareopenaccessarticles
distributedundertheCreativeCommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andrepro-
ductioninanymedium,providedtheoriginalworkisproperlycited.
Editorial Board
MohammadF.Al-Saleh,Jordan DebasisKundu,India ManLaiTang,HongKong
VoV.Anh,Australia MichaelLavine,USA RobertJ.Tempelman,USA
ZhidongBai,China NikolaosE.Limnios,France A.Thavaneswaran,Canada
IshwarBasawa,USA ChunshengMa,USA PetervanderHeijden,TheNetherlands
Shein-chungChow,USA EricMoulines,France RonglingWu,USA
MurrayClayton,USA HungT.Nguyen,USA KelvinK.W.Yau,HongKong
DennisDeanCox,USA MadanL.Puri,USA PhilipL.H.Yu,HongKong
JunbinB.Gao,Australia Jose´ Mar´ıaSarabia,Spain DanielZelterman,USA
ArjunK.Gupta,USA LawrenceA.Shepp,USA RicardasZitikis,Canada
TomaszJ.Kozubowski,USA H.P.Singh,India
Contents
ActuarialandFinancialRisks:Models,StatisticalInference,andCaseStudies,RicˇardasZitikis,
EdwardFurman,AbdelhakimNecir,JohannaNesˇlehova´,andMadanL.Puri
Volume2010,ArticleID392498,3pages
ForestFireRiskAssessment:AnIllustrativeExamplefromOntario,Canada,W.JohnBraun,
BruceL.Jones,JonathanS.W.Lee,DouglasG.Woolford,andB.MikeWotton
Volume2010,ArticleID823018,26pages
TheFoundationsofProbabilitywithBlackSwans,GracielaChichilnisky
Volume2010,ArticleID838240,11pages
Asteroids:AssessingCatastrophicRisks,GracielaChichilniskyandPeterEisenberger
Volume2010,ArticleID954750,15pages
ContinuousTimePortfolioSelectionunderConditionalCapitalatRisk,
GordanaDmitrasinovic-Vidovic,AliLari-Lavassani,XunLi,andAntonyWare
Volume2010,ArticleID976371,26pages
IndividualPropertyRiskManagement,MichaelS.Finke,EricBelasco,andSandraJ.Huston
Volume2010,ArticleID805309,11pages
OnSomeLayer-BasedRiskMeasureswithApplicationstoExponentialDispersionModels,
OlgaFurmanandEdwardFurman
Volume2010,ArticleID357321,19pages
PricingEquity-IndexedAnnuitiesunderStochasticInterestRatesUsingCopulas,
PatriceGaillardetz
Volume2010,ArticleID726389,29pages
LocalLikelihoodDensityEstimationandValue-at-Risk,ChristianGourierouxandJoannJasiak
Volume2010,ArticleID754851,26pages
Zenga’sNewIndexofEconomicInequality,ItsEstimation,andanAnalysisofIncomesin
Italy,FrancescaGreselin,LeoPasquazzi,andRicˇardasZitikis
Volume2010,ArticleID718905,26pages
RiskNavigatorSRM:AnAppliedRiskManagementTool,DanaL.K.HoagandJayParsons
Volume2010,ArticleID214358,17pages
EstimatingL-FunctionalsforHeavy-TailedDistributionsandApplication,AbdelhakimNecir
andDjamelMeraghni
Volume2010,ArticleID707146,34pages
POT-BasedEstimationoftheRenewalFunctionofInteroccurrenceTimesofHeavy-Tailed
Risks,AbdelhakimNecir,AbdelazizRassoul,andDjamelMeraghni
Volume2010,ArticleID965672,14pages
EstimatingtheConditionalTailExpectationintheCaseofHeavy-TailedLosses,
AbdelhakimNecir,AbdelazizRassoul,andRicˇardasZitikis
Volume2010,ArticleID596839,17pages
AnAnalysisoftheInfluenceofFundamentalValues’EstimationAccuracyonFinancial
Markets,HiroshiTakahashi
Volume2010,ArticleID543065,17pages
HindawiPublishingCorporation
JournalofProbabilityandStatistics
Volume2010,ArticleID392498,3pages
doi:10.1155/2010/392498
Editorial
Actuarial and Financial Risks: Models, Statistical
Inference, and Case Studies
Ricˇardas Zitikis,1 Edward Furman,2 Abdelhakim Necir,3
Johanna Nesˇlehova´,4 and Madan L. Puri5,6
1DepartmentofStatisticalandActuarialSciences,UniversityofWesternOntario,London,
ON,CanadaN6A3K7
2DepartmentofMathematicsandStatistics,YorkUniversity,Toronto,ON,CanadaM3J1P3
3LaboratoryofAppliedMathematics,MohamedKhiderUniversity,Biskra07000,Algeria
4DepartmentofMathematicsandStatistics,McGillUniversity,Motreal,QC,CanadaH3A2K6
5DepartmentofMathematicsandStatistics,KingFahdUniversityofPetroleumandMinerals,
Dhahran31261,SaudiArabia
6DepartmentofMathematics,IndianaUniversity,Bloomington,Indiana47405,USA
CorrespondenceshouldbeaddressedtoRicˇardasZitikis,[email protected]
Received10June2010;Accepted10June2010
Copyrightq2010RicˇardasZitikisetal. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and
reproductioninanymedium,providedtheoriginalworkisproperlycited.
Understanding actuarial and financial risks poses major challenges. The need for reliable
approachestoriskassessmentisparticularlyacuteinthepresentcontextofhighlyuncertain
financial markets. New regulatory guidelines such as the Basel II Accord for banking and
Solvency II for insurance are being implemented in many parts of the world. Regulators
in various countries are adopting risk-based approaches to the supervision of financial
institutions.
Many researchers in a variety of areas have been dealing with nontrivial and highly
multifaceted problems in an attempt to answer seemingly plain questions such as how to
assess and quantify risks (cid:2)Crouhy, Galai, and Mark (cid:3)1(cid:4)(cid:5). The present issue of the Journal
of Probability and Statistics provides a glimpse of how challenging such problems are,
both philosophically and mathematically, through a collection of papers that cover a large
spectrumofappliedandtheoreticalproblems.
A number of ideas concerning measuring risks stem from the economic theory and
in particular from the classical utility theory (cid:2)Neumann and Morgenstern (cid:3)2(cid:4)(cid:5) as well as
fromtheprospecttheory(cid:2)KahnemanandTversky(cid:3)3(cid:4)(cid:5),whichweresubsequentlydeveloped
into the anticipated, also known as rank-dependent or generalized expected, utility theory
(cid:2)Quiggin(cid:3)4(cid:4)(cid:5),andmostrecentlyintoaground-breakingtheoryofchoiceunderuncertainty
thatallowsforthepresenceofcatastrophicrisks(cid:2)Chichilnisky(cid:3)5(cid:4)(cid:5).
2 JournalofProbabilityandStatistics
This special Journal of Probability and Statistics issue offers many articles based
on such economic theories and their extensions. G. Chichilnisky develops foundations
for dealing with catastrophic risks, called “black swans”, which require tools beyond the
classicalσ-additiveprobabilitytheory.M.Finke,E.Belasco,andS.Hustonreviewhousehold
propertyriskmanagementtheoryinordertocompareoptimalriskretentiontoconventional
practice. Aided with ideas of behavioral economics and finance, H. Takahashi investigates
theforecastaccuracyoffundamentalvaluesinfinancialmarketsandclarifiesissuessuchas
price fluctuations. F. Greselin, L. Pasquazzi, and R. Zitikis develop statistical inference for
Zenga’sindexofeconomicinequality,whoseconstructionbringstomindtherelativenature
ofnotionssuchassmallandlarge,poorandrich.
To make us aware of the scope and complexity of the problem, several authors have
contributedpaperstacklingriskswithinandbeyondthefinancialsector.G.Chichilniskyand
P.Eisenbergerhavewrittenafar-reachingarticleonasteroidrisks.Theyconvinceusaboutthe
criticalimportanceoftheserisks,forwhichverylittleresearchhasbeencarriedout,andthey
provide an interesting methodology for comparing asteroid risks with the risks of climate
changetomakebetterdecisionsaboutresearchanddevelopment.Forfurtherinformationon
thisandotherrelatedtopics,werefertothewebsitehttp://www.chichilnisky.com/.
W. J. Braun, B. L. Jones, J. S. W. Lee, D. G. Woolford, and M. Wotton examine the
riskassessmentofforestfiresinordertogenerateburnprobabilityriskmaps,concentrating
on the district municipality of Muskoka in Ontario, Canada, as an illustrative example.
D. L. K. Hoag and J. Parsons discuss their new program, Risk Navigator SRM, which
greatly expands the number of managers that can address risks in agriculture. The
program lays down solid foundations and provides state-of-the-art practical support tools,
including a web site (cid:2)http://www.risknavigatorsrm.com/(cid:5), a risk management simulator
(cid:2)http://www.agsurvivor.com/(cid:5),andabookthatputsitalltogether(cid:2)Hoag(cid:3)6(cid:4)(cid:5).
Specific insurance risk-related problems are tackled by a number of authors.
P.Gaillardetzdevelopsanelaborateevaluationapproachtoequity-linkedinsuranceproducts
understochasticinterestrates.O.FurmanandE.Furmanproposelayer-basedcounterpartsof
anumberofriskmeasuresandinvestigatetheirpropertiesandanalytictractability,especially
withintheframeworkofexponentialdispersionmodels.
One of the basic measures of risk is the so-called value-at-risk, which amounts to a
high quantile from the statistical point of view. It is arguably one of the most challenging
measures to estimate and to work with in practice. This risk measure was advocated by
theBaselCommitteeonBankingSupervision(cid:2)http://www.bis.org/bcbs/(cid:5)andimplemented
worldwide.C.Gourie´rouxandJ.Jasiaksuggestanddevelopanovelnonparametricmethod
forestimatingtheconditionalvalue-at-riskandillustrateitsperformanceonreal-lifeportfolio
returns. G. Dmitrasinovic-Vidovic, A. Lari-Lavassani, X. Li, and A. Ware explore the
conditionalcapital-at-riskmeasureinthecontextofportfoliooptimizationandofferoptimal
strategies.
This special Journal of Probability and Statistics issue also includes papers that
develop statistical inference for distortion risk measures and related quantities in the case
of heavy-tailed distributions. A. Necir and D. Meraghni deal with the estimation of L-
functionals, which are generalizations of the distortion risk measure, and which naturally
ariseintheaforementionedanticipatedutilitytheory.A.Necir,A.Rassoul,andD.Meraghni
developatheoryforestimatingtherenewalfunctionofinteroccurrencetimesofheavy-tailed
risks. A. Necir, A. Rassoul, and R. Zitikis introduce a new estimator of the conditional tail
expectation,whichisoneofthemostimportantexamplesofthedistortionriskmeasureand
JournalofProbabilityandStatistics 3
demonstrate the performance of the new estimator within the framework of heavy-tailed
risks.
We, the editors of this special issue, most sincerely thank three groups of people,
without whom this special issue would not have reached its fruition: first and foremost,
the authors who have shared with us their research achievements; second, the helpful and
efficient Hindawi Publishing Corporation staff; third, the professional and diligent referees
whoseeffortsresultedinusefulfeedbackincorporatedintooftenseveralroundsofrevisions
of the herein published papers. We are also grateful to various granting agencies (cid:2)the
Actuarial Foundation, the Actuarial Education and Research Fund, the Society of Actuaries
Committee on Knowledge Extension Research, and the Natural Sciences and Engineering
ResearchCouncilofCanada(cid:5)fortheirsupportofourresearch.
RicˇardasZitikis
EdwardFurman
AbdelhakimNecir
JohannaNesˇlehova´
MadanL.Puri
References
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(cid:3)4(cid:4) J.Quiggin,GeneralizedExpectedUtilityTheory,KluwerAcademic,Dodrecht,TheNetherlands,1993.
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