MathematicalModelingforCopingwithUncertaintyandRisk
MarekMakowski
InternationalInstituteforAppliedSystemAnalysis,A-2361Laxenburg,Austria.marek@iiasa.ac.at,http://www.iiasa.ac.at/marek
Copingwithuncertaintyindecision-making,especiallyforintegratedmanagementofrisk,requirestheanalysisofvariousmeasuresofoutcomesresultingfromapplyingalternativepol-icyoptions.Policyoptionsincludevariousexantemeasures(suchasmitigation,differentar-rangementsforriskspreading)andexpostmeasuresaimedatreducingandsharinglosses.Theoutcomesofimplementingagivensetofpolicymeasuresaretypicallymeasuredbyvariousindicatorssuchasexanteandexpostcosts,benefitsfrommitigationmeasures,welfare,qualityoftheenvironment,andindicatorsofriskexposure(valueatrisk,insolvency).Theamountofdataandrelationshipsforanyriskmanagementproblemarefartoocomplextobeanalyzedbasedsolelyonexperienceand/orintuition.Therefore,mathematicalmodelshavebecomeakeyelementofdecision-makingsupportinvariouspolicyprocesses,especiallythoseaimedatintegratedmanagementofdisasterrisk.
Thischapteroutlinesmethodological,social,andtechnicalproblemsrelatedtothedevelop-mentofnovelmethodsforsuchmodels,andillustratesapplicationsofsuchmethodsbycasestudiesdoneatIIASA.1.Introduction
Everybodyhastocopewithuncertaintyandtomanagevariousrisksinheworldthatischang-ingmoreandmorerapidlyclearlystretchingthesocialfabric.Oneofthedominantdrivingforcesisefficiency,whichhasledtoglobalization,increaseddependencyamongmorediver-sifiedsystems,areductioninmanysafety(bothtechnologicalandsocial)margins,andotherfactorswhichcontributetoincreasedvulnerability.1However,fasterdevelopmenthasitsprice.Traditionalsocietiesdevelopedslowerbutinamorerobustway,i.e.,theconsequencesofwrongdecisionsornaturalcatastropheswerelimitedtorathersmallcommunities.Nowadays,thecon-sequencesofwrongdecisionsmaybewider(evenglobalandlong-term)andmoreserious.Evenatthefamilylevel,fasterdevelopmenthasitsprice.Thereisagreatdealofstresscausedbythedemandtobethebest,amuchlowertoleranceforfailure,andbyvariousrisks(e.g.,asubstantialdecreaseoffuturepension,orofloosingasinglesourceoffamilyincome).Lesspeoplearesuccessfulincompetitivesocietiesthaninegalitariansocieties.Thisisnotonlya
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moralproblembutinthelongertermitreducesthesecurity,safety,andreliabilityofthreetypesofinterlinkedsystems:human,economic,andtechnological.
Asecure,safe,andreliablesocietyrequiresarationalandtimelydecisionmaking.However,decisionmakingisbecomingmoreandmoredifficultbecausedecisionproblemsarenolongerwell-structuredproblemsthatareeasytosolvebyintuitionorexperiencesupportedbyrelativelysimplecalculations.Eventhesametypeofproblemsthatusedtobeeasytodefineandsolve,arenowmuchmorecomplexbecauseoftheglobalizationoftheeconomy,andamuchgreaterawarenessofitslinkageswithvariousenvironmental,social,andpoliticalissues.Moreover,decision-makingisdoneforthefuture,whichalwaysisuncertain.Thus,anydecision-makerneedstocopewithuncertaintyinordertorationallymanagevariousrisks.Rationaldecisionmakingtypicallyrequires:
arepresentationofrelationshipsbetweendecisionsandoutcomes(theconsequencesofap-plyingadecision),
understandingtheuncertaintiesrelatedtovariousrepresentationsofsuchrelationships,
arepresentationofpreferentialstructures(measuresoftradeoffsbetweenvariousoutcomes)ofthestakeholders(personsand/orinstitutionsaffectedbytheconsequencesofimplementingdecisions),
anassessmentofthetemporalandspatialconsequencesofimplementingaselecteddecision,anassessmentofvariousrisksrelatedtoeitherimplementinga(bestatthemoment)decisionorpostponingmakingadecision(untilapossiblybetterdecisioncanbemade),
aprocedure(conventionallycalledDMP–DecisionMakingProcess)forselectingthebestsolution(decision),and
aprocedureforinvolvingstakeholdersintheDMP,andforcommunicatingdecisionstostakeholders.
Itisnotpracticabletoattempttodealwithalltheseissuesforanygivendecisionproblem.Eachoftheseelementshasalargenumberofmethodsandcorrespondingtoolsandanattempttofullyexploitthecapabilitiesofmanyofthemisdoomedtofailure.DifferentdecisionproblemsandtheassociatedDMPhavedifferentcharacteristics,whichcallforfocusingonimplementingaselectionofmethodsandtools.However,therearesomecommoncharacteristicsofmodel-basedsupportfordecisionmaking,andaselectionofthesearediscussedinthischapter.
2.Context
2.1.Commonbackground
Beforefocusingoncopingwithuncertaintyandriskmanagementissuesindecisionmakingforcomplexproblems,letusbrieflyconsidera(theoreticallysimple)commonlyknownandwell-structuredproblem:adecisionbyanindividualtobuyacar.Fromamethodologicalper-spective,thisisamulticriteria(withasmallnumberofcriteria)problemofaselectionfromasmallsetofalternatives.Thealternativesareratherwelldefinedandcriteriaareeasilyinter-pretedbyapersonmakingthedecision.Thereareseveralmethodssupportingdecisionmakinginsuchsituations,andyettheproblemistypicallysolvedusingintuitionandexperienceratherthananyanalyticaltool.Itisinterestingtonotethatthesameproblemissolvedinadifferentwaybydifferentfutureownersofacar,andthesamepersonmaytakeverydifferentdecisionsthatevenhe/shecannotexplainusingthecriteriathatarebelievedtocompletelydefinethetradeoffs.DifferentapproachestakenbydifferentpersonsisexplainedbytheconceptofHabit-
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ualDomainintroducedbyYu[1].Differentsolutions(eachbelievedtobethebest)tothesamechoiceproblemshowthatevenforasimpledecisionproblemitmaybeimpossibletopreciselydefineacompletesetofcriteriaandtradeoffsbetweenthem.
Whileachoiceofacaristypicallydonewithoutusinganyanalyticaltools,intuitionandexperiencealonecannotbeusedfortheanalysisof(typicallyinfinitenumberof)solutionstocomplexproblems.Therefore,moderndecisionmakerstypicallyneedtosomehowintegrateknowledgefromthesevariousareasofscienceandpractice,andthiscanpracticallybedoneonlybyusingamathematicalmodel.Unfortunately,theculture,language,andtoolsdevel-opedforknowledgerepresentationinthekeyareas(suchastheeconomy,engineering,environ-ment,finance,management,socialandpoliticalsciences)areverydifferent.Thisobservationisknowntoeverybodywhohaseverparticipatedinteamworkwithresearchersandpractitionerswhohavebackgroundsindifferentareas.Giventhegreatheterogeneityofknowledgerepresen-tationinvariousdisciplines,andthefastgrowingamountofknowledgeinmostareas,theneedforefficientknowledgeintegrationfordecisionsupportremainsachallengethatdeservestobeaddressed.Moredetaileddiscussionofthesetopicscanbefoundin[2–4].
2.2.Model-baseddecision-makingsupport
Safe,secureandreliablesocietiescannotberealizedwithoutmodel-basedsupportforan-alyzingandsolvingcomplexproblemsorganizedinawaythatistransparentnotonlyforscientistsandexperts.Foranycomplexdecisionproblemmodelsarenecessarynotonlytosupportadecision-makingprocessbutalsotoenhancepublicunderstandingofproblemsandtheproposedsolutions.Asthischapterfocusesonsupportingdecisionmaking,weonlybrieflycommentontheroleofmodelsinpublicinformation.Bynowitiscommonlyagreedthattheprovisionofinformationiscriticaltopublicacceptance,andthatinrealitysomecommonlydiscussedproblemsareactuallyincorrectlyunderstood.Selectedissuesofmodelingforknowl-edgeexchangearediscussedin[3].Therelevanceofthispublicationforpolicymakingisillustratede.g.,bySterman[5],whopointsoutthatalthoughtheKyotoProtocolisoneofthemostwidelydiscussedtopics,mostpeoplebelievethatstabilizingemissionsatnearcurrentrateswillstabilizetheclimate.Currentdebates(someaccompaniedbystrikes)onpensionsystemreformsinseveralEuropeancountriesalsoclearlyshowawidemisunderstandingofthecon-sequencesofpopulationstructuredynamicsoneconomiesingeneralandonpensionsystemsinparticular.These,andmanyotherproblems,canalsobeexplainedtothepublicbyadaptingrelevantmodelsforuseinpresentationsthatthepubliccanunderstand.Unfortunately,variousmodelsdevelopedforpolicy-makingproblemsusedifferentassumptions,andoftendifferentsetsofdata;thereforeacomparativeanalysisoftheirresultscanatbestbedoneandunder-stoodbyasmallcommunityofmodelers.Theneedforpublicaccesstoknowledgepertinenttopolicy-makingwillcertainlygrow,seee.g.,[6],whodiscussesaccesstoenvironmentalin-formation;thustheroleofmodelsinpubliclifewillalsogrowaccordingly.Multidisciplinaryandinterdisciplinarymodelingwillgrowinimportanceforthenextgenerationsociety,seee.g.,[7],forwhichaknowledge-basedeconomywillbecomeamajordrivingforcefordevelopment.Modelscanrepresentknowledgeasbothsynthesizedandstructuredinformation,whichcanbeverifiedbyvariousgroupsofmodelusers,seee.g.,[4,8–10].
Makingrationaldecisionsforanycomplexproblemrequiresvariousanalysesoftradeoffsbetweenconflictingobjectives(outcomes)thatareusedformeasuringtheresultsofapplyingvariouspolicyoptions(decisions).Therearethreeissuesrelatedtoapropermodel-basedsup-
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port:first,developingamodelthatrepresentstherelationsbetweendecisionsandoutcomes,second,supportinganalysesoftradeoffsbetweenconflictingobjectives,andthird,organizingparticipationofstakeholdersinselectedactivitiesofthewholemodelingprocess.
Models,whenproperlydevelopedandmaintainedandequippedwithpropertoolsfortheiranalysis,canintegraterelevantknowledgethatisavailablefromvariousdisciplinesandsources.Whilethesubstanceofvariousenvironmentalmodelsisobviouslydifferent,manymodelingmethodsandportabletoolsformodelgenerationandanalysisareapplicabletoproblemsofdifferentorigins.Manysuchmodelsposeadditionalchallengesowingtothelargeamountofdata,complexrelationsbetweenvariables,thecharacteristicsoftheresultingmathematicalpro-grammingproblems,andrequirementsforcomprehensiveproblemanalyses.Suchchallengeshavemotivatedthedevelopmentofadvancedmodelingtechnologyforsupportingthewholemodelingcycle.Thisincludesmodelspecification,datamanagement,generationofmodelinstances(composedofaselectedmodelspecificationanddatadefiningparametersandsetsforcompoundvariables),variousmethodsofanalysesofinstances,anddocumentationofthewholemodelingprocess.Amodelingtechnologythatsupportsthisapproachtomodel-baseddecision-makingsupportissummarizedinSection3.1.
2.3.Uncertaintyandrisk
Asoutlinedabove,integrationofknowledgeformodel-baseddecisionsupportisacomplexproblemevenwithoutconsideringthetwootherelementsofdecisionmaking,whicharethekeycharacteristicsofmanyproblems,namely,uncertaintyandrisk.
About200yearsagoLaplacearguedthattheworldwascompletelydeterministic,i.e.,ifweknewthecurrentstateofalltheelementsoftheuniverse(fromlargebodiestoatoms)andasetofscientificlaws,thenwecouldpredictallevents(includinghumanbehavior)withcertainty.Thisimpliesthatuncertaintyisaconsequenceofourincompleteknowledgeandwillevaporateifknowledgebecomescomplete.Thisdoctrineofscientificdeterminismwasstronglyresistedbymanypeople,butitremainedthestandardassumptionofscienceforover100yearsuntilasequenceofdiscoveriesinphysicsprovedthatdevelopmentsinsciencecanincreaseuncertainty.In1926Heisenbergprovedthattheproductofthreeattributesofaparticle(theuncertaintyintheposition,theuncertaintyinvelocity,andthemass)canneverbesmallerthanthePlanck’sconstant.Thiswasthefirstproofthatuncertaintycannotbereducedbelowacertainlevel.Since1933Kolmogorovdevelopedprobabilitytheoryinarigorouswayfromfundamentalaxioms;in1954hepublishedafundamentalworkondynamicsystems,wherehealsodemonstratedthevitalroleofprobabilitytheoryinphysics,andofapparentrandomnessinsystemsbelievedtobedeterministic.
Weshoulddistinguishbetweentwotypesofuncertaintyrelatedtoaconsideredphenomena:epistemicuncertainty:duetoincompleteknowledge(whichrangesfromdeterministicknowl-edgetototalignorance)ofthephenomena,
variabilityuncertainty:duetotheinherentvariability(i.e.,naturalrandomness)ofthephe-nomena,e.g.,naturalprocesses;humanbehavior;social,economic,technologicaldynamics;anddiscontinuities(orfastchanges)insomeoftheseprocesses.
Whiletheepistemicuncertaintycanbereducedprovidedthatthereistimeandresourcestodoso,thevariabilityuncertaintyshouldbeadequatelyaddressedinanyrationaldecision-makingprocess.Furtheronwewilldiscussvariabilityuncertaintyforwhichwewillusethetermuncertainty.
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Themostcommontreatmentofthevariabilityuncertaintyisthroughoneofthefollowingthreeparadigmsofprobabilitydefinedas:
ratiooffavorableeventstothetotalnumberofequallylikelyevents(Laplace),
long-runfrequencyoftheevent,iftheexperimentwasrepeatedmanytimes(vonMises),ameasureofasubjectivedegreeofcertaintyabouttheevent(Bayes,Keynes).
Thefirsttwoparadigmsassumethatprobabilityisanattributeofthecorrespondingevent(orobject),thethirdoneisbasedonbeliefs.However,aproperlyusedprobabilityispartoftheadditivesettheorybuiltbyKolmogorovonasetofmathematicalaxioms.Unfortunately,countlessapplicationsofprobabilitytheorydonotconformtotheseaxioms.
Therearetwopitfallswhenusingprobabilityindecisionmakingunderuncertainty:
Incorrectcalculationofprobabilities(e.g.applyingtheLaplace’sparadigmtoeventsthatarenotequallylikely;orviolatingassumptionofvonMisesby:countingfrequencyfromob-servationsofeventsthatoccurredunderdifferentconditions,orbyusingasmallsampleofdata,orbyinterpretingasdataresultsprovidedbyvariousmodelsbasedonrelateddata,orbymultipleuseofthesamedataeachinterpreted2asindependentevents).Probabilitydefinedastherelativefrequencyisequaltothelimitofaninfinitesequence,anditisrarelyprovedtowhatextentitisrelatedtotherelativefrequencyinferredfromafinitesubsetoftheinfinitesequence.
Correctprobabilitiesprovideagoodbasisforfrequentlyrepeateddecisionmakingprovidedneithertheprobabilitydistributionnorpayoffschangesubstantially(becausethisisacondi-tionforagoodapproximationofaninfinitesequenceofdecisionsbyafinitesubsequence),andonewantstooptimizeatotalexpectedoutcome(definedasasumofpayoffsweightedbytheirprobabilities).However,asdemonstratedalreadyin1739byBernoulli’sStPetersburgparadox(seefore.g.,[11]),maximizationofanexpectedoutcome(orutility)isnotrationalforsituationswhereadecisionismadeonlyonce,orwhenforasequenceofdecisionstheconsequencesofeachdecisionshouldbeevaluatedseparately.
Forrationaldecisionmakingunderuncertaintyoneneedstoevaluatetherisksassociatedwithimplementingadecision.Theisnocommonagreement(nottomentionalackofanunderlyingrigorousmathematicaltheory)onthedefinitionofrisk.Weadapthere(after[12])thefollowingdefinition:Riskisasituationoreventinwhichsomethingofhumanvalue(includinghumansthemselves)hasbeenputatstakeandwheretheoutcomeisuncertain.Riskhasawiderangeofconnotations(e.g.,relatedtofears,concerns,uncertainties,thrillsorworries)butthereareunifyingfeaturesthatportraythemeaningofrisk.Whateverthevariationinconnotation,riskimpliesthepossibility(asopposedtoapredetermination)ofsomeoutcome.Riskthusimpliesuncertaintyaboutanoutcome,andcanonlybemeasuredifoneknowsallthepossibleoutcomesandtheprobabilityofeachoutcomeoccurring.
However,measuringriskisstillachallengingproblem,especiallyforrisksrelatedtorareeventswithhighconsequences,conventionallycalledcatastrophicrisksthatarecharacterizedbyso-calledheavy-taildistributions(moreover,suchdistributionsaretypicallymulti-modalandoftentheexpectedvalueoflossescorrespondstoaneventwhichcannotoccur).Toillustratethisproblemletusrecallthatinvestmentriskistypicallymeasuredbyastandarddeviation(denotedby)ofreturnsfromthatinvestment.Standarddeviationisstillcommonlyusedasaprimarymeasureofriskignoringthefactsshowingthatitisoftennotadequate.Forexample,the1929,
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1987,2000/2001stockmarketcrasheswereeachabouta10event;thuseachwould(underGaussianstatistics)onlyhappenonceinthelifetimeofEarth.
Riskisnotonlydifficulttomeasurebutitis(especiallylow-probabilityrisks)difficultforthepublicandmostdecisionmakerstounderstand(seee.g.,[13]).Probablythemostfrequentquestionillustratingthisis:“whyhavewehadthree100-yearfloodsduringthelast10years?”Hencebuildingacommon(forstakeholderswithdifferenthabitualdomains)understandingofriskisanotherchallengingproblem.
2.4.Stakeholders,temporalandspatialscales
Sofarwehavenotconsideredtheotherthreeelementsofdecisionmaking,namelystakeholders,andtemporalandspatialscales.Duetospacelimitationwecanonlyoutlinethescopeofrelatedproblemsbyconsideringtheproblemofclimate,whichisaglobalcommongood.Climatechangeisdrivenbyacombinationofnaturalandanthropogenicprocesses,wherethestrongestimpactofthelatterisafunctionofthecollectiveGHGemissionsandsinksofallindividualsandallhumanactivities.Climatechangeisstillfartoocomplexaproblemtobepreciselymodeled.However,thereisstrongevidencethatanthropogenicactivitiesmaycauseirreversibleandabruptclimatechange.Consequently,thereisgrowingunderstandingfortheneedforactionaimedatlimitingtheanthropogenicimpactonclimatechange.
Althoughtheproblemisglobal,responsibilitiesareplacespecificandliewithallindividuals,privateandpublicorganizations,andallnations.Thesestakeholdershavedifferentcharacteris-tics(e.g.,assets,priorities,obligations),seee.g.,[14].Responsepoliciesandmeasuresarelocalwhiletheconsequencesarelongtermandglobal,andthereforeaconcertedeffortbyallstakeholdersisnecessaryforachievingtheglobalgoalinarationalway.Moreover,therearemanyscientificuncertaintiesrelatedtoclimate,andthereareverydiverseopinionsonthescientifictreatmentofepistemicandvariabilityuncertainties,andontheapproachestoembracingitinthescience-policyinterface(seee.g.,[15,16]),andonassessingandcommunicatinguncertain-tiestothepublic[17].Generally,uncertaintymayjustifyinactionuntilepistemicuncertaintyisreducedthusprovidingabetterbasisformakingmoreefficientdecisions.However,thetimeneededforreducinguncertaintymaybe(infinitely)long,andpostponingsomeactionsmayeitherresultinirreversibleandabruptchangesorwillrequiresubstantiallymoredemandingso-lutions.Whilethereareextremelydifferentopinionsonwhetherornotclimaterelatedactionsshouldactuallybetakenwithoutanyfurtherdelay,theconsequencesofembracinguncertaintyasanexcuseforinactioninotherareasofdecisionmakingarecommonlyknown.
Thelong-timehorizonandtheglobalnatureoftheclimateproblem,togetherwiththescien-tificuncertaintiestheypresent,posespecialchallengesfordecisionmakerswhohavetobalancepotentiallydemandingactionsforavertinggloballong-termrisksagainstothermoreimmediate(andtypicallylocalwithashorttimehorizon)humandevelopmentdemands.Thesethreetypesoftradeoffs(globalvslocal,shorttermvslongterm,uncertainvsperceivedtobecertain)arethemajorchallengesforactualimplementationofthenecessarymeasuresbypoliticians,whoseconstituencieshaveprimarilylocalandshort-termpreferences.Model-baseddecisionsupportistheonlywaytorationallyidentifyvariousmeasuresrelatedtoclimatechange,andtosupportvariousanalysesoftradeoffsbetweenthecostsofthemeasuresandtheirconsequencesforre-ducingtheanthropogenicimpactonglobalchange.Thisistheonlywaytoprovidescientificallybasedandpoliticallyneutralinputtopolicy-makingprocesses,whichneedstobeconductedinaparticipatoryfashion,involvingmanyresearchinstitutionsinteractingwithpotentialusers,
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i.e.,decisionmakers,variousgroupsofexperts,andstakeholders.
2.5.Riskmanagement
Beforediscussingactiveriskmanagementoneshouldpointoutthealternativewait-and-seestrategy,i.e.,hopingthatanunfavorableeventwillnotoccur,andreactonly,ifitindeedwillbethecase.Contrarytocommonbelievessuchastrategymayhaverational(seee.g.[12]forargumentsandcasestudies)explanations.
Activeriskmanagementistypicallycomposedoftwointerrelatedsetsofactions:reducingtheriskbymitigation,adaptation,anddiversificationmeasures,
applyingfinancialinstruments(insurance,hedging,catastrophefunds,contingencycredits,catastrophebonds).
Reducingriskiswellestablishedinwellorganizedsocieties,andinthelongertermitisthemostrationalaction.However,itsimplementationrequiresresourcesandluck(tobeabletoimplementthemeasuresbeforethefirstcatastrophewilloccur).Thereistypicallyalimitbeyondwhichafurtherreductionofriskismoreexpensivethantheapplicationofanappropriatecombinationoffinancialinstruments.Inadditiontotraditionalfinancialinstrumentsthereareideasofanewfinancialorder[18]thataimatanintegratedmanagementofalltypesofeconomicrisk.
Riskmanagementrequirestheanalysisoftradeoffsbetweenoutcomes(criteria)expressedindifferentunits.Themostcommonapproachistoconvert(typicallyforcomputationsonly)suchmulticriteriaproblemintoasingle-criterionoptimizationproblem.Suchanapproachhasseri-ous,butnotcommonlyrecognized,limitations(seee.g.[19]).Thereforeitisworthmentioningatrulymulticriteriaoptimizationofdecisionmakingunderrisk[20].
3.Model-basedsupportforcopingwithuncertaintyandrisk
3.1.Modelingfordecision-makingsupport
Mathematicalmodelingfordecision-makingsupportistheprocessofcreating,analyzing,anddocumentingamodel,whichisanabstractrepresentationofaproblemdevelopedforfind-ingapossiblybestsolutionforadecisionproblem.Theroleofmodelsinmoderndecisionmakingthatissharedbytheauthorofthischapterisdiscussedindetailin[21]alongwiththemethodologyandtoolsformodel-baseddecision-makingsupport,andseveralapplicationstocomplexenvironmentalpolicy-makingproblems.Amorediversifiedcollectionofmethodsandapplicationsispresentedin[22],andamorefocuseddiscussionofselectedelementsofmodelingfordecisionsupport,andanupdatedbibliographyisprovidedin[19].
Amathematicalmodeldescribesthemodeledproblembymeansofvariables,whichareabstractrepresentationsoftheseelementsoftheproblem,whichneedtobeconsideredfortheevaluationoftheconsequencesofimplementingadecision(typicallyrepresentedbyavectorcomposedofmanyvariables).Moreprecisely,suchamodelistypicallydevelopedusingthefollowingconcepts:
decisions(inputs),whicharecontrolledbytheuser;
externaldecisions(inputs),whicharenotcontrolledbytheuser;
outcomes(outputs),usedformeasuringtheconsequencesofimplementationofinputs;relationsbetweendecisionsand,andoutcomes;suchrelationsaretypicallypresentedintheform:
(1)
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whereisavectoroffunctions.
Theconciseformulation(1)ofamodelspecification3maybemisleadingforthosewhoareunawareofthecomplexityoftheprocessofmodelspecification.Eachmodelrepresentsapartofknowledgethatisrelevantforanalysisofthegivendecisionproblem.Thus,themodelmustbeconfinedtoawell-definedareaofinterest,itcanonlybevalidforaspecificpurpose,andtherealphenomenaisalwaysonlypartiallytorepresentedbythemodel.Consider,forexample,modelingacupofcoffee.Verydifferentmodelsaresuitableforstudyingvariousaspects,e.g.,howsomething(sugar,cream)isdissolvedinthecup’scontent,orunderwhatconditionsthecupmightbreakfromthermalstresses,orwhatshapeofcupismostsuitableforuseinaircraft,orhowacupofcoffeeenhancesdifferentpeople’sproductivity.Anattempttodevelopamodeltocoveralltheseaspects,andrepresentalltheaccumulatedknowledgeonevensuchasimpletopicwouldnotberational.
Todefineapurposeformodelingoneneedstoanalyzeifandhowamodelcancontributetofindingabettersolutionthatcanbefoundwithoutamodel.This,inturn,implicitlysetstherequirementsforaselectionofinputandoutputvariables,andaspecificationoffunctions(1)thatdefinerelationsbetweenvariables.Becauseoftheunquestionablesuccessofmodelinginproblemsolving,variousmodelingparadigmshavebeenintensivelydevelopedoverthelastfewdecades.Thus,differenttypesofmodels(characterizedbytypesofvariablesandrelationsbetweenthem)weredeveloped(e.g.,static,dynamic,continuous,discrete,linear,nonlinear,de-terministic,stochastic,set-membership,fuzzy,softconstraints)withaviewtobestrepresentingdifferentproblemsbyaselectedtypeofmodel.Eachmodelingparadigmembodiesagreatdealofaccumulatedknowledge,expertise,methodology,andmodelingtoolsspecializedforsolvingvariousproblemspeculiartoeachmodelingparadigm.
Althoughseveralwell-developedmodelingparadigmsexistitisnoteasytoselecttheonethatisthebestfortheproblemathand.Moreover,foraselectedparadigmamodelermustfindawayofavoidingtoomuchdetailwhilepreservingtheessentialfeaturesofthespecificproblem.Finally,evenforaselectedsetofvariablesandrelationsthereareoftenseveralwaysofintroducingauxiliaryvariablesanddefiningtherelations,whichmightbeequivalent(i.e.,theresultsofthemodelanalysisshouldbethesame4)butdifferentspecificationsmayresultinsubstantialdifferencesinefficiencyofthewholemodelingprocess(especially,whendifficultoptimizationproblemsaresolvedduringthemodelanalysis,seee.g.,[22,23]).
Thus,anappropriatemodelspecificationforanynon-trivialproblemrequiresacombinationofknowledge,experience,intuition,andtaste.Therefore,modelingremainsandwillremainanart.Morediscussionontheartofmodelingcanbefoundin[24].
However,notonlymodelspecificationbutalsoitsuseindecision-makingprocessisamorecomplexissuethantypicallyperceived.Inparticular,modelanalysisisprobablytheleast-discussedelementofthemodelingprocess.Thisresultsfromthefocusthateachmodelingparadigmhasonaspecifictypeofanalysis.However,theessenceofmodel-baseddecision-makingsupportispreciselytheopposite;namely,tosupportvariouswaysofmodelanalysis,andtoprovideefficienttoolsforcomparisonsofvarioussolutions.Thus,weoutlinenowaway
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inwhichamodelthatadequatelyrepresentstherelationsbetweenthedecisionsandtheout-comes(usedformeasuringthecorrespondingconsequences)canbeusedforfindingdecisionsthatfitbestthepreferencesofthedecisionmakers.
Figure1.Atypicalstructurewhenusingamathematicalmodelfordecision-makingsupport.
Atypicalstructurewhenusingmodelsfordecision-makingsupportisillustratedinFigure1.ThebasicfunctionofDecisionSupportSystem(DSS)istosupporttheuserinfindingvaluesofhis/herdecisionvariablesthatwillresultinasolutionoftheproblemthatfitsbesttothepreferencesoftheuser.
Atypicaldecisionproblemhasaninfinitenumberofsolutions,andusersareinterestedinthosethatcorrespondbesttotheirpreferencesrepresentedherebyapreferentialstructure
oftheuser.Apreferentialstructuretakesdifferentformsfordifferentwaysofmodel
analysis,e.g.,for:
Classicalsimulation,itiscomposedofgivenvaluesofinputvariables;
Softsimulation,itisdefinedbydesiredvaluesofdecisions,andbyameasureofthedistancebetweentheactualanddesiredvaluesofdecisions;
Singlecriterionoptimization,itisdefinedbyaselectedgoalfunctionandbyoptionaladdi-tionalconstraintsfortheother(thanthatselectedasthegoalfunction)outcomevariables;Multicriteriamodelanalysis,itisdefinedbyanachievementscalarizingfunction,whichrep-resentsthetradeoffsbetweenthecriteriausedfortheevaluationofsolutions.
Apreferentialstructuretypicallyinducespartialorderingofsolutionsobtainedfordifferentcombinationsofvaluesofinputs,andinawell-organizedmodelingprocesspreferentialstruc-tureisnotincludedinthemodel,butisdefinedduringthemodelanalysisphase,whenuserstypicallymodifytheirpreferencessubstantially.Infact,awell-organizedmodelanalysisphaseiscomposedofseveralstages,seee.g.,[19],eachservingdifferentneeds;thus,typically,notonlyaredifferentformsofusedforthesameproblembutalsodifferentinstancesofeachoftheseformsaredefineduponanalysisofpreviouslyobtainedsolutions.
Suchanapproachtousemodelsforsupportingdecisionmakingdifferssubstantiallyfromthe(traditional)ORroutineofrepresentingadecisionproblemasamathematicalprogrammingproblem,e.g.,intheform:
(2)
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whichprovidesoptimaldecisions.Countlessnumberofactualapplicationsshows,however,thatformostcomplexproblemsitisnotpossibletoadequatelydefinea(thatrepre-sentspreferencesofdecisionmakers)norasetoffeasiblesolutions.Infact,varioustypesofmathematicalprogrammingproblemsaretypicallydefinedduringtheanalysisphase;thus,optimizationcontinuestoplayacrucialroleinmodel-baseddecisionsupport.However,opti-mizationinsupportingdecisionmakingforsolvingcomplexproblemshasquiteadifferentrolefromitsfunctioninsomeengineeringapplications(especiallyreal-timecontrolproblems)orinveryearlyimplementationsofORforsolvingwell-structuredmilitaryorproductionplanningproblems.Thispointhasalreadybeenmadeclearlye.g.,byAckoff[25],andbyChapman[26],whocharacterizedthetraditionalwayofusingORmethodsforsolvingproblemsascomposedofthefollowingfivestages:describetheproblem;formulateamodeloftheproblem;solvethemodel;testthesolution;andimplementthesolution.Theshortcomingsofsuchanapproacharediscussedinmanyotherpublications,someofwhichareoverviewedin[21].
Thus,model-basedsupportfordecision-makingforcomplexproblemshastomeetmuchmoredemandingrequirements(thanthoseadequateforproblemsoftype(2),whicharead-equateforwell-structured,relativelysimpledecisionproblems)fortheunderlyingmodelingprocess,whichisbyfarmorecomplexthanaprocessofmodeldevelopmentforwell-structureddecisionproblems.Theserequirementsdemandalsoanewtechnologyofmodeling,suchastheStructuredModelingTechnology(SMT)discussedindetailin[27].
Modelsfortheintegratedmanagementofcatastrophicriskarenotonlycomplexbutalsopossessspecificfeatures,whicharediscussedbelow.Thus,theirpresentationbelowservestwopurposes.First,itillustratestheactualcomplexityofsuchmodelsandjustifiesthereasonswhythegeneral-purposemodelingtools,andthetraditionalORapproachtomodelanalysiscannotbesuccessfulinsuchcases.Second,itprovidesenoughdetailsaboutsuchmodelsandthecorrespondingmodelingprocesstohelpinthedevelopmentofthistypeofapproachforsupportingdecision-makingprocessforsimilartypeofproblems.
3.2.Integratedcatastrophicriskmanagement3.2.1.Background
Catastrophicriskmanagementisacomplexinterdisciplinaryproblemrequiringknowledgeofenvironmental,natural,financial,andsocialsystems.Theirburdenisunevenlydistributed,debatableinscope,andyetnotwellmatchedtopolicymakers.Adecision-makingprocessre-quirestheparticipationofvariousagentsandstakeholders:individuals,governments,farmers,producers,consumers,insurers,investors,etc.Theperceptionbyalltheseactorsofcatastro-phes,goalsandconstraintswithrespecttotheserare/highconsequenceeventsisverydiversi-fied.Thescarcityofhistoricaldataisaninherentfeatureandamajorchallengeindesigningstrategiesfordealingwithrarecatastrophes.Thus,catastrophicriskscreatenewscientificprob-lemsrequiringintegratedapproaches,newconcepts,andtoolsforriskmanagement.Theroleofmodelsenablingthesimulationofpossiblecatastrophesandestimatingpotentialdamagesandlossesbecomesakeytaskfordesigningmitigationandadaptationprograms.
Belowweoutlinethemodeldevelopedforsupportinganintegrateddecision-makingprocess.Thismodelsupportstheanalysisofspatialandtemporalheterogeneityofvariousagents(stakeholders)inducedbymutuallydependentlossesfromextremeevents.Themodeladdressesthespecificsofcatastrophicrisks:limitedinformation,theneedforlongtermperspectivesandgeo-graphicallyexplicitmodels,andamulti-agentdecision-makingstructure.Themodelcombines
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geographicallyexplicitdataonthedistributionofcapitalstocksandeconomicvaluesininfras-tructureandagricultureinaregionwithastochasticmodelgeneratingmagnitudes,occurrences,andlocationsofcatastrophes.Usingadvancedstochasticoptimizationtechniques,themodel,ingeneral,supportsthesearchfor,andtheanalysisofrobustoptimalportfoliosofexante(landuse,structuralmitigation,insurance)andexpost(adaptation,rehabilitation,borrowing)measuresfordecreasingregionalvulnerabilitymeasuredintermsofeconomic,financial,andhumanlossesaswellasintermsofselectedwelfaregrowthindicators.
3.2.2.TheintegratedcatastrophemanagementmodelThemodelconsistsofthreemajorsubmodels:acatastrophemodule,
anengineeringvulnerabilitymodule,andaneconomicmulti-agentmodule.
Thecatastrophemodulesimulatesnaturalphenomenonusingamodelbasedontheknowl-edgeofthecorrespondingtypeofevent,whichisrepresentedbyasetofvariablesandrelationsbetweenthem.Forexample,forahurricanemodelthevariablesaretheradiusofthemaximumwinds,ortheforwardspeedofthestorm.Foranearthquakemodelthatsimulatestheshakingofthegroundtheseareepicenter’slocation,magnitudesofearthquakes,G¨utenberg-Richterlaws,orattenuationcharacteristics.Forafloodtheseareprecipitationcurves,waterdischarge,rivercharacteristics,etc.ThecatastrophemodelsusedinIIASA’scasestudiesarebasedonMonteCarlodynamicsimulationsofgeographicallyexplicitcatastrophepatternsinselectedregions(adiscussionofthesemodelsisbeyondthescopeofthischapterbutcanbefounde.g.,in[28–34]).Acatastrophemodel,infact,compensatesforthelackofhistoricaldataontheoccurrenceofcatastrophesinlocationswheretheeffectsofcatastrophesmayhaveneverbeenexperiencedinthepast.
Theengineeringmoduleisusedtoestimatethedamagesthatmaybecausedbythecatastro-phes.Shakingintensities,durationofstandingwater,waterdischargespeedorwindspeedsarewhatengineeringmodulestakefromthecatastrophemodulestocalculatepotentialdamages.Theengineeringmodulesusevulnerabilitycurvesandtakeintoaccounttheageofthebuilding,andthenumberofstoriesinordertoestimatethedamagesinducedbythesimulateddisaster.Theeconomicmulti-agentmodelusedinourcasestudiesisastochasticdynamicwelfaregrowthmodel(see,e.g.,[35]).Thismodelmapsspatialeconomiclosses(whichdependonim-plementedlossmitigatingandsharingpolicyoptions)intogainsandlossesofagents:acentralgovernment,amandatorycatastropheinsurance(acatastrophepool),aninvestor,individuals(cellsorregions),producers(farmers),etc,,
CatastropheandvulnerabilityGIS-basedmodelingcoupledwithmulti-agentmodelsisstillnotwidelyused.However,itisbecomingincreasinglyimportant:
togovernmentsandlegislativeauthoritiesforbettercomprehending,negotiatingandmanag-ingrisks;
toinsurancecompaniesformakingdecisionsontheallocationandvaluesofcontracts,pre-miums,reinsurancearrangements,andtheeffectsofmitigationmeasures;
forhouseholds,industries,farmersforrisk-basedallocationofpropertiesandvalues;forscientificcommunitiesinvolvedinglobalchangeandsustainabilityresearch.
Acatastrophecanruinmanyagentsiftheirriskexposuresarenotappropriate.Todesignsafecatastrophicriskmanagementstrategiesitisnecessarytodefinelocationspecificfeasible
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decisionsbasedonpotentiallossesgeneratedbyacatastrophemodel.Someofthesedecisionsreducethefrequencies(likelihood)andmagnitudesofcatastrophicevents(say,land-usedeci-sions)andredistributelossesandgainsatlocalandinternationallevels(say,pools,insurance,compensationschemes,credits).Differentcatastrophicscenariosingeneral,lead,todifferentdecisionstrategies.Thenumberofalternativedecisionsmaybeverylarge,andthestraightfor-wardif-thenevaluationofallalternativesmayeasilyrequiremorethan100years.
3.2.3.AdaptiveMonteCarlooptimization
Theimportantquestionishowtoby-passlimitationsoftheif-thenanalysisandfindacombi-nationofstrategies,whichwouldbethe”best”strategyforallpossiblecatastrophes.In[35]itwasshownthatthesearchfor”robust”optimaldecisionscanbedonebyincorporatingstochas-ticSpatialAdaptiveMonteCarlooptimizationtechniquesintocatastrophicmodelingthaten-ablesthedesignofdesirablerobustsolutionswithoutevaluatingallpossiblealternatives.Themodeliscomposedofelementswiththefollowingfunctionality:
InitialvaluesforpolicyvariablesareinputintotheCatastropheModel.
TheCatastropheModelgeneratescatastrophesandinduceddirectandindirectdamages.Theefficiencyofthepoliciesisevaluatedwithrespecttotheperformanceindicatorsoftheagents,e.g.,insurers,insured,governments,etc.
Ifthesedonotfulfilltherequirements,goalsandconstraints,theyarefurtheradjustedintheAdaptiveFeedbackssubmodel.Inthismanneritispossibletotakeintoaccountcomplexinterdependenciesbetweendamagesatdifferentlocations,availabledecisionsandresultinglossesandclaims.
Thecrucialquestionistheuseofappropriateriskindicators(measures,metrics),e.g.,toavoidbankruptciesofagents.Catastrophiclossesoftenhavemultimodaldistributions,andthereforetheuseofmeanvalues(e.g.,expectedcostsandprofits)maybemisleading.Roughlyspeaking,wecannotthinkintermsofaggregateregionallossesandgainsasthesumoflocationspecificlossesandgains(e.g.,ifthemeanvalueissubstitutedbythemedian).Inourmodelweapplyeconomicallysoundriskindicatorssuchasbankruptcyofinsurers,expectedshortfallofinsur-ers’riskreserve,andoverpaymentsandunderpaymentsbyindividuals.Theseindicatorsareusedtogetherwithso-calledstoppingtimestodirecttheanalysistowardsthemostdestructivescenarios.
3.2.4.Casestudies
Theadequacyoftheoutlinedmethodologywastestedinanumberofcasestudies.Initsfirstapplication,theintegratedmodelanalyzedtheinsurabilityofrisksintheIrkutskregioninRussia,whichisexposedtotheriskofearthquakes(seee.g.[28,31])resultsdemonstratedthemodel’scapabilityofgeneratinginsurancestrategiesthatarerobustwithrespecttodependen-ciesanduncertaintiesinducedbythecatastrophes,thusreducingtheriskofbankruptcytotheinsurers.
Thesecondcasestudy(seee.g.,[36])inaseismic-proneItalianregionillustratedtheneedforajointeffortbymultiplestakeholdersinmanagingthecatastrophes.Itemphasizedthatneitherthemarketnorthegovernmentmaybeconsideredastheefficientmechanismforcatastrophicriskmanagement.Onlysomeformofapublic-privatepartnershipwouldbeappropriate.Also,itillustratedthatthepolicyoptionssuggestedbystakeholdersmayoftenbemisleadingandresultinevenhigherlosses.Onlycomprehensivemodel-basedanalysisofdependenciesbetweenthetimingofcatastrophesoccurrences,damages,claims,goals,andconstraintsofagentscanassist
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towardsloss-reductionmanagement.
Inthethirdcasestudy[32],theintegratedmodelevaluatedaninsuranceprogramformitigat-ingandsharinglossesduetoseverefloodsintheUpperTiszaregioninHungary.Inthisstudyspecialattentionwasgiventotheevaluationofstrategiesrobustagainstavarietyoffloods.Suchstrategiesarecomposedofapublicmulti-pillarfloodloss-spreadingprograminvolvingpartialcompensationtofloodvictimsbythecentralgovernment,thepoolingofrisksthroughmanda-torypublicinsuranceonthebasisoflocation-specificexposures,andacontingentexantecredittoreinsurethepool’sliabilities.Acomplementary(morefocusedonsocialandpolicy-makingissues)descriptionofthiscasestudyisgivenin[37].4.Uncertainty,risk,andmodernsocieties
Afterdiscussingthemethodologicalbackgroundofmodel-basedsupportforriskmanage-ment,andpresentinginmoredetailoneselectedapproachandrelatedapplications,wesumma-rizeotherIIASA’sresearchactivitiespertinenttoriskmanagement.
TheRisk,Modeling,andSocietyProjecthasalonghistoryofresearchontheeconomicandsocialimplicationsoftechnological,health,andotherriskstomodernsocieties.Majorprojectshavebeencarriedoutonthisbroad,interdisciplinarytopic,including:theperceptionofriskstotechnologicaldisasters,theinstitutionalaspectsofriskpolicymaking[38],theequityissuesofsitinglocallyunwantedfacilities[39],andtheroleofexpertiseinriskpolicymaking[40].Recentactivitiesfocusonthedesignofinstrumentsandmodel-baseddemocraticproceduresforeffectivelyandequitablyreducingandredistributingtherisksofextremeevents,withspecialemphasisontransitionanddevelopingcountries.Asurveyofglobalexperiencewithrespecttothefinancialaspectsofdisastersshowsthatthevictimsofextremenaturalevents,despiteinsur-anceandpublicsolidarity,areprimarilythehouseholdsandbusinessessufferingthelosses[38].AprojectfundedbytheBritishAssociationofInsurerscarriedout7casestudiesofmajordisas-tersinAsia,Europe,andtheUS,whichshowedthatcountrypracticesdiffergreatlyonhowthefinancialrisksareabsorbed,whetherprivatelythroughinsurancearrangementsand/orpubliclythroughsocialsolidarity.Thisstudyalsoinvestigatedtheincentivelinksbetweenrisksharingandpreventivemeasurestoreducethelosses.
Thisthemeofrisksharingandlossreductionforextremeeventshasnowbecometopicalatthegloballevel,especiallysincetheIPCCpredictionthatextremeweathereventswillworsenwithclimatechange.Acurrentconcernishelpingdevelopingandtransitioncountriesadapttoweatherextremes.Manygovernmentsofpoorcountriesfacebudgetaryrestrictionsinreducingdisasterlossesandprovidingpostdisasterreliefandreconstruction,andgovernmentsofverypoorandverydisaster-pronecountries,forexample,Honduras,thePhilippines,andChina,facesuchenormousrisksthatregionscanbesetbackyearsintheirdevelopment.IncollaborationwiththeInter-AmericanDevelopmentBank,IIASAhascontributedtothedevelopmentofaproactive,integrateddisasterriskmanagementstrategy[41]withspecialemphasisondevelop-ingtoolsforthefinancialmanagementoftheserisks,andexploringwhetherdisasterhedgescouldbecomeanewformofassistancefromtheNorthtotheSouth[42].
Howrisksarereducedandsharedisavalue-laden,policyissue,whichwasaddressedbytheriskassessmentprojectformanagingfloodrisksintheUpperTiszariverbasin.Thisactivitycombinedinformationtechnology(presentedinSection3.2)withpublicparticipationthroughstakeholderinterviews,surveys,andstakeholderworkshops[43,44].
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Theworkonriskfinancingintransition-anddevelopingcountrieshasrecentlyreceivedrecognitionintheclimatenegotiationscommunity,inparticularintheUNFCCCactivitiesoninsuranceandriskassessmentinthecontextofclimatechangeandextremeweatherevents.Moreover,theIIASAmodel-basedresearchonfinancialriskmanagementisnowusedincol-laborativeactivitieswiththeWorldBankandtheInter-AmericanDevelopmentBanktotakeaccountofcatastrophiceventsincountrydevelopmentplans.
IIASAhasalsomadeseveralactivitiesaddressingproblemsofsocialsecurity.Here,weoutlineonlytheoptimization-basedanalysisofsocialsecurityunderuncertaintiesandrisks.Inmostcasesthesocialsecuritysystemisthemaindeterminantofpopulationwelfare.Dom-inatinginmajorOECDcountriesthePAYG(pay-as-you-go)systemisnowadaysputunderstressbyrapidlychangingdemographicconditions,aging,characterizedbyloweringfertilityandincreasinglongevity.Besidesthis,instabilitiesinfinancialmarkets,economicdistress,in-flationanddevaluationoftenproducegraveimpactsonsourcesfinancingretirement.Majorquestionstoexploreare:
Whatisessentialfortheefficientfunctioningofthesystem?
Cantheexistingsystemssurviveinthecurrentdemographicandeconomicenvironment?HowcanthetransitionfromPAYGtofundedpensionsystemswork?
InmanyOECDcountriesacombinationofthePAYGandfundedpensionsystemsisbe-ingdiscussed.Criteriaforevaluationofvariouscombinationsinclude:theleastcostforthetransition,theleastburdenonvariouspopulationgroups(e.g.,retirees,andcontributorstothesystems),theleastcostlyfinancialmeasurestoaidthetransition,forexample,throughinterna-tional/nationalborrowing.
Thebroadrangeofuncertaintiesinherenttosocialsecurityproblemsnecessitatetheexplicitintroductionandtreatmentofuncertaintiesandrisksintothesocialsecuritysimulationmodel,andtheformulationanddevelopmentofanoptimizationbasedapproachtotheanalysisofsocialsecuritysystems[45,46].
Thesocialsecuritysimulationmodel[45]isacompromisebetweenapurelyactuarialmodelandanoverlappinggenerationsgeneralequilibriummodel.Itdealswithproductionandcon-sumptionprocessescoevolvingwithbirth-and-deathprocessesofinvolvedagents,e.g.,region-specifichouseholdssubdividedintosingle-yearagegroups,firms,governments,financialin-termediaries,includingpensionsystemsandinsurance.Theproductionfunctionofthemodelallowstotrackincomesexpenditures,savingsanddissavingsofagents,aswellasintergener-ationalandinterregionaltransfersofwealth.Thestochasticoptimizationapproach[46]com-binesthismodeltogetherwitharollinghorizonstochasticoptimizationprocedurewhichallowstoexplicitlyandrealisticallytreattheunderlyinguncertaintieswiththegoalofmaximizingso-cialwelfare(consumptionofworkersandretirees)byfine-tuningthemixofthetransferbasedPAYGandcapitalreservefinancefundedsocialsecurityschemes.
ThesocialsecuritysimulationmodelofIIASAwasappliedinamultidisciplinarystudyofpopulationaginginJapan[47].ThisstudywasmadepossiblebyfinancialsupportfromtheEconomicandSocialResearchInstituteoftheJapaneseCabinetOfficeaspartofitsMilleniumProject.Thegeneralconclusionsofthestudiesareslowingpercapitagrowth,adecliningna-tionalsavingrate,risingsocialcontributionrates(subjecttotheassumptionofnochangeinlaborforceparticipationratesorthecalculationofpension,health,andlong-termcarebene-fits),andreductioninnetforeignassets.Whiledisposableincomeofboththeelderlyandtheworking-agepopulationareexpectedtorise(i.e.,livingstandardswillcontinuetoimprove),the
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assumptionsofthemodeltranslateintoaneventualdeclineinthelivingstandardsoftheyoungrelativetothoseoftheelderly.Thisis,ofcourse,subjecttoourassumptionthatthemainmech-anismforadaptingtotherisingcostsofpensionsandhealthisincreasingpayrollcontributionrates.ThispictureistypicalforallrapidlyagingregionsoftheworldamongwhichJapanmaybeleadingtheway,butothercountriesmustsurelyfollow.
WeclosethisoverviewofselectedIIASA’sactivitiesrelatedtotreatmentofuncertaintyandtoriskmanagementbyprovidingreferencestoselectedpublications(butnotrepeatingpublica-tionsalreadycitedinthischapter)addressingpertinentmethodologicalissues:Anintroductiontomeasuringrisk[48].Newmeasuresofrisk[49].
Stochasticoptimizationfordesignofcatastrophicrisksportfolios[50–52].Tradeoffsbetweensecurityandgrowth[53].
Exanteandexpostfinancialstabilizationoflongtermgrowth[54].Catastrophicriskmanagement[55].
Theroleofinsuranceinrisktransfer[56].Modelingforfinancialoptimization[57].Numericsoffinancialmanagement[58].
5.Conclusions
Copingwithuncertainty,andrationalriskmanagementforanycomplexdecision-makingsituationisacomplexprocess,andtherearenosimple(andadequate)solutionstotrulycomplexproblems.Moreover,theimpactofinadequateriskmanagementmaybenotonlysignificantbutalsoglobal.Complexityandglobalimpactrequiretwotypesofcooperation:
amongstakeholdersatdifferentlocationsandofdifferenttype(centralandlocalgovernments,enterprises,NGO’s,individuals);
betweenresearchersfromvariousfieldsthatneedtocontributetobuildingobjective,model-basedsupportfordecision-support.
Thereisawealthofknowledgeandexperiencethatcancontributetorationalriskmanage-ment.However,theseresourcesarefragmented,andofteninincompatibleforms.Integratingsuchresourcesispartofawider,andevenmorechallengingproblem,namelyintegratingfrag-mentedknowledgetoappropriatelyservetheknowledgesociety.Thisnewtypeofsocietycanactuallybesafe,secure,andreliableonly,ifdecisionsonvariouslevelswillbemadeinacon-certedwayusingintegratedknowledge.
Duetotheunquestionablesuccessofmodelinginproblemsolving,variousmodelingpar-adigmshavebeenintensivelydevelopedoverthelastfewdecades.Inthis,toagreatextentcasestudydrivenprocess,agrowingtendencytofocusonspecificmethodologiesandtoolswasobserved.Eachmodelingparadigmembodiesalotofaccumulatedknowledge,expertise,methodology,andmodelingtoolsspecializedforsolvingmanyoftheproblemsbelongingtoeachmodelingparadigm.However,theseresourcesarefragmented,andusingmorethanoneparadigmforaproblemathandistooexpensiveandtimeconsuminginpractice.TheStruc-turedModelingofGeoffrionprovidesamethodologyforunifyingdifferentparadigms,andforstructuringthemodelingprocess,whichisthenecessaryconditionforeffectivemodelingofcomplexsystems.TheStructuredModelingTechnology(SMT)providesmodulartoolsforstructuredmodeling,andsupportsalsothekeyrequirementsforgoodmodelingpractice,see
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e.g.,[5,21,22,25,27,59–62]foradiscussionofvariouskeyelementsofsuchpractices,andofsometypicalmodelingpitfalls.
Modeling,especiallyoflargeand/orcomplexproblemsrequiresacombinationofknowledge,craft,andart.Model-basedsupportforpolicymakingissuesisbyfarmorecomplexthanmodelingforsolvingbetter-structuredproblems,e.g.,inengineeringapplications.Notonlyaremodelsforpolicymakingmorecomplexthanmodelsofwell-structuredproblems,buttherearemoredemandingrequirementsforthewholemodelingprocess,whichinturnneedstobetransparentandwelldocumented.
Thischapteraimsatsharingtheknowledgeandexperiencedevelopedduringthelong-termdevelopmentofseveralcomplexmodels,andatprovidingbasicinformationaboutseveralactu-allyapplicationsofmodel-basedsupportforcopingwithuncertaintyandrisk,andaboutSMTwhichsupportsthewholemodelingprocessformodel-baseddecision-makingsupport.SMTrespondsalsotothechallengingrequirementsforthemodelingprocess,whichwillbegrow-inginthenearfuturewhenmoreandmorepolicy-makingprocesseswillutilizemodel-basedproblemanalysisanddecision-makingsupport.
Finally,thischapterprovidesanextensivelistofreferencesthataimtoprovidepointersforfurtherreadingforthosenewtosomeoftheconceptspresentedandwhomaythereforefindthepresentationtoosketchy.Acknowledgments
TheworkreportedinthischapterhasbeendonebytheRisk,ModelingandSocietyProjectatIIASAincollaborationwithotherIIASAprojects,andseveralinstitutionsandcolleagues,includingtheteamledbyProf.NorioOkadaoftheDisasterPreventionResearchInstituteatKyotoUniversity.Itisimpossibletogivecredittoallcolleagueswhocontributedtothere-portedresearchalthoughthecitationshavebeenmadewheneveritwaspracticabletodoso.However,theauthorwouldalsoliketoacknowledgethosecontributionswhichhadthelargestimpactonthereportedresearchbymentioninginalphabeticalorder:A.Amendola,Y.Ermoliev,T.Ermolieva,J.Linnerooth-Bayer,G.Pflug.Moreover,theauthoracknowledgesthecontribu-tionsofT.Ermolievatothewrite-upforSection3.2,andofJ.Linnerooth-Bayer,T.Ermolieva,andG.PflugforSection4.
TheauthorthanksalsoA.Beulens,A.Geoffrion,J.Granat,H.Scholten,H-J.SebastianandA.P.WierzbickiformanydiscussionsandjointactivitiesonvariousmodelingissuesthathavecontributedalsotothedevelopmentofmodelingmethodologyexploitedinSMT.REFERENCES
1.P.Yu,HabitualDomains:FreeingYourselffromtheLimitsonYourLife.Kansas:Highwa-terEditions,ShawneeMission,1995.
2.M.Makowski,“Knowledgeintegrationinmodel-baseddecisionsupport,”inProceedings
ofInternationalSymposiumonKnowledgeandSystemSciences:ChallengestoComplexity(E.Shimemura,Y.Nakamori,J.Gu,andT.Yoshida,eds.),pp.43–56,Ishikawa,Japan:JapanAdvancedInstituteofScienceandTechnology,2000.ISBN4-924861-09-X.
3.A.WierzbickiandM.Makowski,“Modelingforknowledgeexchange:Globalaspects
ofsoftwareforscienceandmathematics,”inAccesstoPubliclyFinancedResearch(P.WoutersandP.Schr¨oder,eds.),pp.123–140,Amsterdam,theNetherlands:NIWI,2000.
17
4.M.MakowskiandA.Wierzbicki,“Modelingknowledgeinglobalinformationnetworks,”
in4thGlobalResearchVillageConference.ImportanceofICTforResearchanScience:SciencePoliciesforEconomiesinTransition,(Warsaw),pp.173–186,KBN(thePolishStateCommitteeforScientificResearch),andOECD(theOrganizationforEconomicCo-operationandDevelopment),InformationProcessingCentre,2003.draftversionavailablefromhttp://www.iiasa.ac.at/˜marek/pubs/prepub.html.
5.J.Sterman,“Allmodelsarewrong:reflectionsonbecomingasystemsscientist,”Systems
DynamicsReview,vol.16,no.4,pp.501–531,2002.
6.M.Haklay,“Publicaccesstoenvironmentalinformation:past,presentandfuture,”Com-puters,EnvironmentandUrbanSystems,vol.27,pp.163–180,2003.
7.P.Drucker,“Thenextsociety,asurveyofthenearfuture,”TheEconomist,,vol.361,
no.8246(Nov.3),pp.3–22,2001.
8.W.Borst,“Constructionofengineeringontologiesforknowledgesharingandreuse,”tech.
rep.,UniversityofTwente,Enschede,TheNetherlands,1997.
9.B.FunkeandH.Sebastian,“Knowledge-basedmodelbuildingwithKONWERK,”Work-ingPaperWP-96-105,InternationalInstituteforAppliedSystemsAnalysis,Laxenburg,Austria,1996.
10.M.Mannino,B.Greenberg,andS.Hong,“Modellibraries:Knowledgerepresentationand
reasoning,”ORSAJournalonComputing,vol.2,pp.1093–1123,1990.
11.P.Anand,FoundationsofRationalChoiceunderRisk.Oxford:OxfordUniversityPress,
1993.
12.C.Jaeger,O.Renn,E.Rosa,andT.Webler,Risk,Uncertainty,andRationalAction.Lon-don:EarhscanPublications,2001.
13.P.SternandH.FIneberg,eds.,UnderstandingRisk:InformingDecisionsinaDemocratic
Society.Washington,D.C.:NationalAcademyPress,1996.
14.A.Najam,ed.,Environment,Development,andHumanSecurity:PerspectivesfromSouth
Asia.NeyYork,Oxford:UniversityPressofAmerica,2003.
15.H.Pollack,UncertainScience...UncertainWorld.Cambridge:CambridgeUniversity
Press,2003.
16.A.KinzigandD.Starrett,“Copingwithuncertainty:Acallforanewscience-policyforum,”
AMBIO,AJournaloftheHumanEnvironment,vol.32,no.5,pp.330–335,2003.
17.A.Petersen,P.Janssen,J.vanderSluijs,J.Risbey,andJ.Ravetz,“RIVM/MNPguid-anceforuncertaintyassessmentandcommunication,”TechnicalReportIR-03-02,RIVM,Bilthoven,TheNetherlands,2003.
18.R.Shiller,TheNewFinancialOrder,Riskinthe21thCentury.Princeton,Oxford:Prince-tonUniversityPress,2003.
19.M.MakowskiandA.Wierzbicki,“Modelingknowledge:Model-baseddecisionsupport
andsoftcomputations,”inAppliedDecisionSupportwithSoftComputing(X.YuandJ.Kacprzyk,eds.),vol.124ofSeries:StudiesinFuzzinessandSoftComputing,pp.3–60,Berlin,NewYork:Springer-Verlag,2003.ISBN3-540-02491-3,draftversionavailablefromhttp://www.iiasa.ac.at/˜marek/pubs/prepub.html.
20.W.Ogryczak,“Multiplecriteriaoptimizationanddecisionunderrisk,”ControlandCyber-netics,vol.31,no.4,pp.975–1003,2002.
21.A.Wierzbicki,M.Makowski,andJ.Wessels,eds.,Model-BasedDecisionSupportMethod-ologywithEnvironmentalApplications.Series:MathematicalModelingandApplications,
18
Dordrecht:KluwerAcademicPublishers,2000.ISBN0-7923-6327-2.
M.Makowski,“Modelingtechniquesforcomplexenvironmentalproblems,”inNaturalEnvironmentManagementandAppliedSystemsAnalysis(M.MakowskiandH.Nakayama,eds.),pp.41–77,Laxenburg,Austria:InternationalInstituteforAppliedSystemsAnalysis,2001.ISBN3-7045-0140-9.
W.Ogryczak,“Anoteonmodelingmultiplechoicerequirementsforsimplemixedintegerprogrammingsolvers,”Computers&OperationsResearch,vol.23,pp.199–205,1996.J.Paczy´nski,M.Makowski,andA.Wierzbicki,“Modelingtools,”inWierzbickietal.[21],pp.125–165.ISBN0-7923-6327-2.
R.Ackoff,“Thefutureofoperationalresearchispast,”JournalofORSociety,vol.30,no.2,pp.93–104,1979.
C.Chapman,“MytwocentsworthonhowORshoulddevelop,”JournalofOperationalResearchSociety,vol.43,no.7,pp.647–664,1992.
M.Makowski,“Structuredmodelingtechnology,”EJOR,2004.(toappear).
A.Amendola,Y.Ermoliev,T.Ermolieva,V.Gitits,G.Koff,andJ.Linnerooth-Bayer,“Asystemsapproachtomodelingcatastrophicriskandinsurability,”NaturalHazardsJournal,vol.21,no.2/3,pp.381–393,2000.
S.Baranov,B.Digas,T.Ermolieva,andV.Rozenberg,“Earthquakeriskmanagement:Scenariogenerator,”InterimReportIR-02-025,InternationalInstituteforAppliedSystemsAnalysis,Laxenburg,Austria,2002.
K.Christensen,L.Danon,T.Scanlon,andP.Bak,“Unifiedscalinglawforearthquakes,”Proceedings99/1,NationalAcademyofSciences,US,2002.
Y.Ermoliev,T.Ermolieva,G.MacDonald,andV.Norkin,“Stochasticoptimizationofin-suranceportfoliosformanagingexposuretocatastrophicrisks,”AnnalsofOperationsRe-search,vol.99,pp.207–225,2000.
T.Ermolieva,Y.Ermoliev,J.Linnerooth-Bayer,andA.Vari,“IntegratedmanagementofcatastrophicfloodrisksintheUpperTiszabasin:Adynamicmulti-agentadaptiveMonteCarloapproach,”inProceedingsoftheSecondAnnualIIASA-DPRIMeetingIntegratedDisasterRiskManagement:MegacityVulnerabilityandResilience,Laxenburg,Austria:InternationalInstituteforAppliedSystemsAnalysis,2002.http://www.iiasa.ac.at/Research/RMS.
G.Walker,“Currentdevelopmentsincatastrophemodelling,”inFinancialRisksManage-mentforNaturalCatastrophes(N.BrittonandJ.Oliver,eds.),pp.17–35,Brisbane,Aus-tralia:GriffithUniversity,1997.
K.Froot,TheLimitedFinancingofCatastropheRisk:andOverview.Harvard:HarvardBusinessSchoolandNationalBureauofEconomicResearch,1997.
T.Ermolieva,“Thedesignofoptimalinsurancedecisionsinthepresenceofcatastrophicrisks,”InterimReportIR-97-068,InternationalInstituteforAppliedSystemsAnalysis,Laxenburg,Austria,1997.
A.Amendola,Y.Ermoliev,andT.Ermolieva,“Earthquakeriskmanagement:Acasestudyforanitalianregion,”inProceedingsofSecondEuroConferenceonGlobalChangeandCatastropheRiskManagement:EarthquakeRisksinEurope,pp.267–295,Lax-enburg,Austria:InternationalInstituteforAppliedSystemsAnalysis,2000.http://www.iiasa.ac.at/Research/RMS.
L.Brouwers,“SpatialanddynamicmodelingoffloodmanagementpoliciesintheUpper
22.
23.24.25.26.27.28.
29.
30.31.
32.
33.
34.35.
36.
37.
19
Tisza,”InterimReportIR-03-02,InternationalInstituteforAppliedSystemsAnalysis,Lax-enburg,Austria,2003.
J.Linnerooth-Bayer,R.L¨ofstedt,andG.Sj¨ostedt,TransboundaryRiskManagementinEurope.London:Earthscan,2000.
H.Kunreuther,J.Linnerooth-Bayer,andK.Fitzgerald,“Citinghazardousfacilities:Lessonsfromeuropeandamerica,”inEnergyEnvironmentandtheEconomy:AsianPer-spectives(P.Kleindorfer,H.Kunreuther,andD.Hong,eds.),pp.145–167,Brookfield:EdwardElgar,1996.
J.Linnerooth-Bayer,“Climatechangeandmultipleviewsoffairness,”inFairWeather?EquityConcernsinClimateChange(F.Toth,ed.),pp.267–295,London:Earthscan,1999.P.Freeman,L.Martin,J.Linnerooth-Bayer,R.Mechler,S.Saldana,K.Warner,andG.Pflug,“Nationalsystemsforcomprehensivedisastermanagement:Financ-ingreconstruction.phaseIIbackgroundstudyfortheregionalpolicydialogueoftheInter-AmericanDevelopmentBank,”tech.rep.,Inter-AmericanDevelopmentBank,Washington,D.C.,2002.http://www.iadb.org/int/drp/ing/Red6/Docs/FreemanSistemasNatPhase2May20%02eng.pdf.
H.KunreutherandJ.Linnerooth-Bayer,“Thefinancialmanagementofcatastrophicfloodrisksinemerging-economycountries,”RiskAnalysis,vol.23,pp.627–639,2003.
A.Vari,J.Linnerooth-Bayer,andZ.Ferencz,“StakeholderviewsonfloodriskmanagementinHungary’sUpperTiszabasin,”RiskAnalysis,vol.23,pp.583–601,2003.
J.Linnerooth-BayerandA.Amendola,“Specialeditiononfloodrisksineurope,”RiskAnalysis,vol.23,pp.537–627,2003.
T.Ermolieva,A.Westlund,andL.MacKellar,“Onlong-termforecastingofsocialsecurity:arobustnessanalysis,”QualityandQuantity,vol.35,pp.33–48,2001.
T.Ermolieva,“Optimizatinofsocialsecuritysystemsunderuncertainty,”InterimReportIR-02-077,InternationalInstituteforAppliedSystemsAnalysis,Laxenburg,Austria,2002.L.MacKellar,T.Ermolieva,D.Horlacher,andL.Mayhew,EconomicImpactsofPopulationAginginJapan.Brookfield:EdwardElgarPublishing,2004.(forthcoming).
G.Pflug,Howtomeasurerisk?FestschriftforF.Ferschl.Berlin:PhysicaVerlag,1997.G.Pflug,“Someremarksonthevalue-at-riskandtheconditionalvalue-at-risk,”inProb-abilisticConstrainedOptimization-MethodologyandApplications(S.Uryasev,ed.),pp.272–281,Dordrecht:KluwerAcademicPublishers,2000.
Y.Ermoliev,T.Ermolieva,G.MacDonald,andV.Norkin,“Insurabilityofcatastrophicrisks:Thestochasticoptimizationmodel,”Optimization,vol.47,no.3-4,2000.
Y.ErmolievandS.Flam,“Findingparetooptimalinsurancecontracts,”TheGenevaPapersonRiskandInsuranceTheory,vol.26,pp.155–167,2001.
Y.ErmolievandV.Norkin,“Onnonsmoothanddiscontinuousproblemsofstochasticsys-temsoptimization,”EuropeanJournalofOperationResearch,vol.101,pp.230–244,1997.P.FreemanandG.Pflug,“Infrastructureindevelopingandtransitioncountries:Riskandprotection,”RiskAnalysis,vol.3,no.23,pp.601–610,2003.
Y.Ermoliev,T.Ermolieva,andV.Norkin,“Economicgrowthundershocks:Pathdepen-denciesandstabilization,”inMicroMesoMacro:AddressingComplexSystemsCouplings(H.Liljenstr¨omandU.Svedin,eds.),(Abisco,Sweden),AbiscoBook,2004.(forthcom-ing).
Y.ErmolievandV.Norkin,“Riskandextendedexpectedutilityfunctions:Optimizationap-
38.39.
40.41.
42.43.44.45.46.47.48.49.
50.51.52.53.54.
55.
20
proaches,”InterimReportIR-03-033,InternationalInstituteforAppliedSystemsAnalysis,Laxenburg,Austria,2003.
G.Pflug,“Riskreshapingcontractsandstochasticoptimization,”CentralEuropeanJournalofOR,vol.5,no.3-4,pp.205–230,1998.
G.Pflug,E.Dockner,A.Swietanowski,andH.Moritsch,“TheAURORAfinancialman-agementsystem:frommodeldesigntoparallelimplementation,”AnnalsofOperationsResearch,vol.99,pp.189–206,2000.
G.PflugandA.Swietanowski,“Selectedparalleloptimizationmethodsforfinancialman-agementunderuncertainty,”ParallelComputing,vol.26,pp.3–25,2000.
A.Geoffrion,“Anintroductiontostructuredmodeling,”ManagementScience,vol.33,no.5,pp.547–588,1987.
M.Pidd,“Justmodelingthrough:Aroughguidetomodeling,”Interfaces,vol.29,no.2,pp.118–132,1999.
Y.NakamoriandY.Sawaragi,“Complexsystemsanalysisandenvironmentalmodeling,”EJOR,vol.122,no.2,pp.178–189,2000.
R.vanWaveren,S.Groot,H.Scholten,F.vanGeer,H.W¨osten,R.Koeze,andJ.Noort,GoodModellingPracticeHandbook.Utrecht,TheNetherlands:STOWA,1999.http://waterland.net/riza/aquest/gmpuk.pdf).
56.57.
58.59.60.61.62.
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