数学中国国际赛论文参考模版 3.docx

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数学中国国际赛论文参考模版3

第二届“认证杯”数学中国

数学建模国际赛

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A

参赛队员（签名）：

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朱凡

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金乔

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刘家栋

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刘保东

第二届“认证杯”数学中国

数学建模国际赛

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（请各个参赛队提前填写好）：

1273

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RiskManagementBasedonModelingRisk

inEconomicSystem

Abstract：

Accordingtothetargetofeconomicsystem,theprocessofvaluerealizationfortheeconomicactivitiesinaneconomicsystemwasanalyzed.

Thenthedefinitionof“risk”insucheconomicsystemswasprovided,andtheimpactofitscomponents:

“riskevents”,“riskfactors”,and“riskgenes”wasanalyzed.Basedontherelationsofriskpotentialandriskevents,thehigh-levelriskmodelwasdeveloped.

Furthermore,basedontherelationof“riskfactors”and“riskgenes”,themodelforanalyzinglow-levelriskinaneconomicsystemwasdeveloped.Thehigh-levelandlow-levelmodelsarecoordinatedbytheinteractionofriskeventsandriskfactors.Therearemanyfactorscausearisk,passtobeengagedintoactuallysetout,aftersurveyedthebasicmarketdataandusedthehigh-levelandthelowlevelasaframework.Alsooneofthemostimportantaspectofrisk--marketriskarediscussed.Inthediscussionofmarketriskmanagement,volatilitymodelingandvortfolioriskarereferred.

Furthermore,operationalriskandregulationmanagementisanalyzed,usinghedgefundsasanexample.Inthediscussionofthispart,BaselIIframeworkandhedgefundduediligencearereferred.

Withthismodel,theriskanalysiscandealwithlargeamountofinformationofdifferentlevels,whilefocusingonparticularconcernsatthesametime.

Keywords:

Marketdata,riskevents,riskfactors,riskgenes,marketrisk,

volatilitymodeling,portfoliorisk,covarianceestimation

Contents

1.Introduction……………………………………………………………………3

1.1economiccalamity………………………………………………………3

1.2Themathematicalmodelintherisk…………………………………………3

1.3Theproblemsofmathematicalmodel………………………………………3

2.TheDescriptionofProblem……………………………………………………4

2.1Howdowedefinetherisk……………………………………………………4

2.1.1Thecharacteristicsofrisk…………………………………………4

2.1.2Fromtheangleofapplicableobject………………………………4

2.2Originalsofthefinancial/economiccrises…………………………………5

2.3Theclassificationoffinancialrisk…………………………………………5

2.4Otherhumanfactorsonrisk…………………………………………………5

3.Models…………………………………………………………………………6

3.1BasicModel.………………………………………………………………6

3.1.1SymbolsandDefinitions………………………………………………6

3.1.2Assumptions…………………………………………………………7

3.1.3TheFoundationofModel………………………………………………7

3.1.4SolutionandResult…………………………………………………19

3.1.5AnalysisoftheResult…………………………………………………19

3.1.6StrengthandWeakness…………………………………………………20

4.Conclusions………………………………………………………………………20

5.References………………………………………………………………………21

6.Appendix………………………………………………………………………22

6.1Statistics………………………………………………………………………22

6.2lettertothefinancialinvestmentfirms………………………………………25

I.Introduction

Inordertoindicatetheoriginoftheeconomiccalamity,thefollowingbackgroundisworthmentioning.

1.1economiccalamity

Theglobalfinancialcrisisthatbeganinsummer2007hascontinuedtowreakdevastatinglossanddamageacrossallmarkets,alleconomies,andallcountries.AninitialliquiditycontractioninthefinancialmarketswastransformedintoafullsolvencycrisisfollowingthecollapseofLehmanBrothersonSeptemberIS,2008.Thiscrisiswasalmostwhollyunpredictedandledtoamassivecollapseingrowthandinvestmentacrosstheworld.Leadingemergingmarketswerenotimmuneasanypossibledecouplingorseparationevaporated.[1FinancialCrisis-U.K.PolicyandRegulatoryResponseWalker,GeorgeA.TheInternationalLawyer44.2]Ineffectivesupervision,questionableinvestmentsandpooroperationsoffinancialinstitutions,andinsodoinghighlighttheneedforanewfinancialregulatoryframeworkthatwilladdresstheseproblemsandrebuildthepublic’sconfidenceinthefinancialindustryasawhole.

1.2Themathematicalmodelintherisk

The2007creditcrisiswasawake-upcallwithrespecttomodelusage.Ithasbeenallegedthatthemisuseofriskmanagementmodelshelpedtogeneratethecrisis.

Themodelsweresupposedtosimulatethecomplexinteractionsofmanymarketforcesononeanother,includingfluctuationsinmarkets,changinginterestrates,pricesofvariousstocks,bonds,optionsandotherfinancialinstruments.Eveniftheydidthat--that'sarguable--theyfailedtoaccountforoneimportantscenario:

Whathappenswheneverybodywantstosellalltheirholdingsatthesametime?

ThisispreciselywhathappenedinthosedarkdaysofSeptember2008,whentheU.S.governmentdecidednottobailoutLehmanBrothers,andthevenerableinstitutiondefaultedonitscreditors.Thedominoeffectofcollapsewasavertedonlybymassiveinfusionsofmoneyfromthefederalgovernment.

1.3Theproblemsofmathematicalmodel

Throughtheriskmodelsindicatedthatthechanceofanymajorinstitutiondefaultingwasminimal.Abigproblemwasthatthemodelsomittedamajorvariableaffectingthehealthofaportfolio:

liquidity,ortheabilityofamarkettomatchbuyersandsellers.Amissingkeyvariableisabigdeal--anequationthatpredictsanairplaneflight'sriskofarrivinglatewillnotbeveryreliableifithasnomathematicaltermrepresentingweatherdelays.

Therearemultiplereasonsforastateoftheeconomy.Blamingtheeconomiccalamityonriskmodelswouldbeanoversimplification.Thereareotherhumanfactors--politicalandregulatorones--certainlycameintoplay.

II.TheDescriptionoftheProblem

2.1Howdowedefinetherisk

Theconceptofriskisanoutgrowthofoursociety'sgreatconcernaboutcopingwiththedangersofmodernlife.Riskreferstothepossibilityofaneventaboutwhatwedon'twanttoconsequences.

1）Thecharacteristicsofrisk

Financialmarketsarebecomingincreasinglysophisticatedinpricing,isolating,repackaging,andtransferringrisks.Toolssuchasderivativesandsecuritizationcontributetothisprocess,buttheyposetheirownrisks.Weareseekingageneraldefinition.Anygeneraldefinitionmustcompassallofsituations.Thesituationsmayappeardisparate,buttheysharecertaincommonelements.First,peoplecareabouttheoutcomes.Ifsomeonehasapersonalinterestinwhattranspires,thatpersonisexposed.Second,peopledon’tknowwhatwillhappen.Ineachsituation,theoutcomeisuncertain,Itseemsthatriskentailstwoessentialcomponentsandsomesmalleraspect:

●Objectivity

●Controllability

●Identifiability

●Accumulation

●Loss

●Thelikelihoodoftheevents

●theuncertaintyofoccurrencetime

●theuncertaintyoftheresult

Basedontheabove,onecandrawaconclusionthatiftheriskisuncertain,theresultofariskmayleadtolostprofit,.likefinancialriskBelong.

2）Fromtheangleofapplicableobject

Riskisaconditionofindividuals--humansandanimals--thatareself-aware（3）.Organizations,companies,andgovernmentsareconduitsthoughwhichindividuals--members,investors,employees,andsuch--takerisk.Lookingthroughacompanytoseewhoultimatelybearsspecificriskscanbeenlightening.Forexample,increasingtheaccountabilityofmanagersincreasescareerriskforthosemanagersbuttendstoreducepriceriskforstockholders.

2.2Originalsofthefinancial/economiccrises

Therearemanyoriginalsofeconomiccalamity,economicpolicymistakes,rawmaterialsnervous,naturaldisasters,theconsequencesofglobalization.Thefinancialpolicyerrors.Fromthepicture1,originalsofthefinancial/economiccrisesissimpletounderstand.

Picture1originofthefinancial/economicscrises

2.3Theclassificationoffinancialrisk

Ingeneral,factorsoffinancialriskcanbedividedintotwoparts:

●Objectivefactors.Forfinancialinstitutions,thisriskisobjectiveexistenceandnottransferwiththewillingofthepeople.Includingcountryrisk,interestraterisk,exchangeraterisk,policyrisk,liquidityrisk,creditrisk,investmentrisk,etc.,mostriskscausedbynon-artificialfactors;

●Subjectivefactors,suchasmanagementrisk,etc.Thereasonsarethatthesalesmanmakesomemistakesinadvertently,mismanagement,laxsupervision.Theseproblemsareinevitabletosomeextent.

2.4Otherhumanfactorsonrisk

Unfortunately,missingilliquidityriskwasn'ttheonlymajorproblem.Financialriskmodelshavebeendesignedtofocusontheriskfacedbyanindividualinstitution.Thatalwaysseemedtomakesensebecauseinstitutionsareconcernedonlywiththeirownrisk,andregulatorsassumedthatiftherisktoeachindividualinstitutionislow,thenthesystemissafe.Buttheassumptionturnedouttobepoor,saysRamaCont,directorofColumbiaUniversity'sCenterforFinancialEngineering.Inasystemwheremanyinterdependentcomponentseachhavealowriskoffailure,henotes,systemicriskcanstillbeexcessive.Imagine30peoplewalkingsidebysideacrossafieldwiththeirarmsaroundoneanother'sshoulders--anyonepersonmaybeunlikelytostumble,butthere'sadecentchancesomeoneinthegroupwill,andthatonestumblercouldbringdownachunkoftheline.That'sthesituationfinancialinstitutionsarein,Contsays."Upthrough2008,regulatorsweren'tconsideringtheconnectionsbetweenthesebanksinassessingrisk,"heobserve