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简介：ThepaperprovidesanapproachofvaluinganP&Dinvestmentopportunity.Theresultshowsthatwhentheinvestmentopportunityvalueisdependentsonthevalueofaproject,wecanuseNPVoftheprojectcompletedtovaluetheoptionofinvestmentotherthantousingofpartialdifferentialequation.Meanwhilethepaperoffersanalternativewaytofindtheoptimalinvestmentrule.

简介：Thispaperconsidersaworst-caseinvestmentoptimizationproblemwithdelayforafundmanagerwhoisinacrash-threatenedfinancialmarket.Drivenbyexistingofcapitalinflow/outflowrelatedtohistoryperformance,weinvestigatetheoptimalinvestmentstrategiesundertheworst-casescenarioandthestochasticcontrolframeworkwithdelay.Thefinancialmarketisassumedtobeeitherinanormalstate(crash-free)orinacrashstate.InthenormalstatethepricesofriskyassetsbehaveasgeometricBrownianmotion,andinthecrashstatethepricesofriskyassetssuddenlydropbyacertainrelativeamount,whichinducestoadroppingofthetotalwealthrelativetothatofcrash-freestate.Weobtaintheordinarydifferentialequationssatisfiedbytheoptimalinvestmentstrategiesandtheoptimalvaluefunctionsunderthepowerandexponentialutilities,respectively.Finally,anumericalsimulationisprovidedtoillustratethesensitivityoftheoptimalstrategieswithrespectivetothemodelparameters.

简介：Aninsurance-packageisacombinationbeingtie-inatleasttwodifferentcategoriesofinsuranceswithdifferentunderwriting-yield-rate.Inthispaper,theoptimalinsurance-packageandinvestmentproblemisinvestigatedbymaximizingtheinsurer’sexponentialutilityofterminalwealthtofindtheoptimalcombination-shareandinvestmentstrategy.Usingthemethodsofstochasticanalysisandstochasticoptimalcontrol,theHamilton-Jacobi-Bellman(HJB)equationsareestablished,theoptimalstrategyandthevaluefunctionareobtainedinclosedform.Bycomparingwithclassicalresults,itshowsthattheinsurance-packagecanenhancetheutilityofterminalwealth,meanwhile,reducetheinsurer’sclaimrisk.

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简介：UsingtheGARCHmodeltodescribetheriskyasset'sreturnprocesssothatitstime-varyingmomentsandconditionalheteroskedasticitycanbeproperlyreflected,generalmultiperiodoptimalinvestmentandconsumptionproblemswithbothfixedandproportionaltransactionscostsareinvestigatedinthispaper.Wemodelthiskindofdifficultproblemsasadynamicstochasticoptimizationproblem,whichcancopewithdifferentutilityfunctionsandanynumberoftimeperiods.Theproceduretosolvetheresultingcomplexnonlinearstochasticoptimizationproblemisdiscussedindetailandabranch-decompositionalgorithmisdevised.

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简介：Intheexistingelectricitymarket,thetraditionalpowersuppliersandrenewableenergygeneratorscoexistinthepowersupplyside.Inthepowersupplyside,renewableenergygeneratorsgeneratepowerbywindandothernaturalconditions,leadingrenewableenergyoutputacertainrandomness.However,thelowmarginalgeneratingcostandthereductionofcarbonemissions,andthusbringsacertainadvantageforrenewableenergycomparedtoalternativeenergy.Electricity,asaspecialcommodity,stableandadequatepowersupplyisanecessaryguaranteeforeconomicandsocialdevelopment.Powershortagesituationisnotallowedinthepowersystem,andtheextrapowerneedstobehandledforthepurposeofsafety.Inthispaper,thehybridpowergeneratedbyrenewableenergygeneratorsandtraditionalenergygeneratorsisusedaspowersupply,andthentheelectricitymarketsellshybridpowertoelectricityconsumers,thehybridpowersystemdeterminestheoptimaldaytimeprice,nighttimeprice,andtheoptimalinstalledcapacityoftherenewableenergysuppliers.Wefindthattheinstalledcapacityofrenewableenergyincreasesfirstandthendecreaseswiththeincreaseofthepricesensitivitycoefficientoftraditionalenergysupply.Electricitydemandisnegativelyrelatedtoelectricitypriceinthecurrentperiod,andispositivelyrelatedtopriceintheotherperiod.Theaveragepriceofdayandnightisonlyrelatedtothetotalpotentialdemandofdayandnightandthetotalgenerationprobabilityofrenewableenergy.Thepricedifferencebetweendaytimeandnighttimeispositivelyrelatedtopotentialelectricitydemand,andnegativelyrelatedtothesensitivitycoefficientofelectricityprice.

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