內容簡介
《隨機金融概要(英文版)》為金融數學和工程數學的讀者提供了機率統計的基本觀點和隨機分析市場風險的分析方法。書中不僅涵蓋了金融中能夠運用到的機率內容，也介紹了數學金融中的最新進展。既講述了金融理論又結合金融實踐，脈絡清晰流暢。每部分的講解從特殊到一般，從實例到結果。綜合性強，包含了數學金融、熵以及馬爾科夫理論。第二部分的學習需要對隨機微積分知識有相當的了解。目次：第一部分：事實，模型：主要概念、結構和工具，金融理論目標和問題以及金融工程；隨機模型，離散時間；隨機模型，連續時間；金融數據統計分析；第二部分：理論：隨機金融模型中的套利原理，離散時間；隨機金融模型中的價格理論，離散時間；隨機金融模型中的隨意理論，連續時間；隨機金融模型中的價格理論，連續時間。目錄
ForewordPart1.Facts.Models
ChapterIMainConcepts，Structures，andInstruments.AimsandProblemsofFinancialTheoryandFinancialEngineering
1.Financialstructuresandinstruments
1a.Keyobjectsandstructures
1b.Financialmarkets
1c.Marketofderivatives.Financialinstruments
2.Financialmarketsunderuncertainty.C1assicaltheoriesofthedynamicsoffinancialindexes，theircriticsandrevision.Neoc1assicaltheories
2a.Randomwalkconjectureandconceptofefficientmarket
2b.Investmentportfolio.Markowitzsdiversification
2c.CAPM：CapitalAssetPricingModel
2d.APT：arbitragePricingTheory
2e.Analysis，interpretation，andrevisionofthec1assicalconceptsofefficientmarket.I
2f.Analysis，interpretation，andrevisionofthec1assicalconceptsofefficientmarket.Ⅱ
3.Aimsandproblemsoffinancialtheory，engineering，andactuarialcalcu1ations
3a.Roleoffinancialtheoryandfinancialengineering.Financialrisks
3b.Insurance：asocialmechanismofcompensationforfinanciallosses
3c.Ac1assicalexampleofactuarialcalcu1ations：theLundberg-Cram6rtheorem
ChapterⅡStochasticModels.DiscreteTime
1.Necessaryprobabilisticconceptsandseveralmodelsofthedynamicsofmarketprices
1a.Uncertaintyandirregu1arityinthebehaviorofprices.Theirdescriptionandrepresentationinprobabilisticterms
1b.Doobdecomposition.Canonicalrepresentations
1c.Localmartingales.Martingaletransformations.Generalized
martingales
1d.gaussianandconditionallyGaussianmodels
1e.binomialmodelofpriceevolution
1f.Modelswithdiscreteinterventionofchance
2.Linearstochasticmodels
2a.MovingaveragemodelMA(q)
12b.AutoregressivemodelAR(p)
12c.AutoregressiveandmovingaveragemodelARMA(p，q)andintegratedmodelARIMA(p，d，q)
12d.Predictioninlinearmodels
3.NonlinearstochasticconditionallyGaussianmodels
3a.ARCHandGARCHmodels
3b.EGARCH，TGARCH，HARCH，andothermodels
3c.Stochasticvo1atilitymodels
4.Supplement：dynamicalchaosmodels
4a.Nonlinearchaoticmodels
4b.Distinguishingbetweenchaoticandstochasticsequences
ChapterⅢStochasticModels.ContinuousTime
1.Non-Gaussianmodelsofdistributionsandprocesses.
1a.Stableandinfinitelydivisibledistributions
1b.Levyprocesses
1c.Stableprocesses
1d.hyperbolicdistributionsandprocesses
2.Modelswithself-simi1arity.Fractality
2a.Hurstsstatisticalphenomenonofself-simi1arity
2b.Adigressiononfractalgeometry
2c.Statisticalself-simi1arity.FractalBrownianmotion
2d.FractionalGaussiannoise：aprocesswithstrongaftereffect
3.ModelsbasedonaBrownianmotion
3a.Brownianmotionanditsroleofabasicprocess
3b.Brownianmotion：acompendiumofc1assicalresults
3c.StochasticintegrationwithrespecttoaBrownianmotion
3d.It5processesandITSSformu1a
3e.Stochasticdifferentialequations
3f.ForwardandbackwardKolmogorovsequations.Probabilisticrepresentationofsolutions
4.Diffusionmodelsoftheevolutionofinterestrates，stockandbondprices
4a.Stochasticinterestrates
4b.Standarddiffusionmodelofstockprices(geometricBrownianmotion)anditsgeneralizations
4c.Diffusionmodelsofthetermstructureofpricesinafamilyofbonds
5.Semimartingalemodels
5a.Semimartingalesandstochasticintegrals
5b.Doob-Meyerdecomposition.Compensators.Quadraticvariation
5c.itSsformu1aforsemimartingales.Generalizations
ChapterⅣStatisticalAnalysisofFinancialData
1.Empiricaldata.Probabilisticandstatisticalmodelsoftheirdescription.Statisticsofticks.
1a.Structuralchangesinfinancialdatagatheringandanalysis
1b.Geography-re1atedfeaturesofthestatisticaldataonexchangerates
1c.Descriptionoffinancialindexesasstochasticprocesseswithdiscreteinterventionofchance
1d.Onthestatisticsofticks
2.Statisticsofone-dimensionaldistributions
2a.Statisticaldatadiscretizing
2b.One-dimensionaldistributionsofthelogarithmsofre1ativepricechanges.DeviationfromtheGaussianproperty
andleptokurtosisofempiricaldensities
2c.One-dimensionaldistributionsofthelogarithmsofrelativepricechanges.Heavytailsandtheirstatistics
2d.One-dimensionaldistributionsofthelogarithmsofre1ativepricechanges.Structureofthecentralpartsofdistributions
3.Statisticsofvo1atility，corre1ationdependenceandaftereffectinprices
3a.Vo1atility.Definitionandexamples
3b.periodicityandfractalstructureofvo1atilityinexchangerates
3c.Corre1ationproperties
3d.Devo1atization.Operationaltime
3e.Clusterphenomenonandaftereffectinprices
4.StatisticalR/S-analysis.
4a.SourcesandmethodsofR/S-analysis
4b.R/S-analysisofsomefinancialtimeseries
Part2.Theory
ChapterV.TheoryofArbitrageinStochasticFinancialModelsDiscreteTime
1.Investmentportfolioona(B，S)-market
1a.Strategiessatisfyingba1anceconditions
1b.Notionofhedging.UpperandlowerpricesCompleteandincompletemarkets
1c.Upperandlowerpricesinasingle-stepmodel
1d.CRR-model：anexampleofacompletemarket
2.Arbitral：e-freemarket
2a.Arbitrageandabsenceofarbitrage
2b.MartingalecriterionoftheabsenceofarbitrageFirstfundamentaltheorem
2c.MartingalecriterionoftheabsenceofarbitrageProofofsufficiency
2d.MartingalecriterionoftheabsenceofarbitrageProofofnecessity(bymeansoftheEsscherconditionaltransformation)
2e.ExtendedversionoftheFirstfundamentaltheorem
3.Constructionofmartingalemeasures
bymeansofanabsolutelycontinuouschangeotmeasure
3a.Maindefinitions.Densityprocess
3b.DiscreteversionofGirsanovstheorem.ConditionallyGaussiancase
3c.MartingalepropertyofthepricesinthecaseofaconditionallyGaussianandlogarithmicallyconditionallyGaussiandistributions
3d.DiscreteversionofGirsanovstheorem.Generalcase
3e.Integer-valuedrandommeasuresandtheircompensators.Transformationofcompensatorsunderabsolutelycontinuouschangesofmeasures.Stochasticintegrals.
3f.predictablecriteriaofarbitrage-free(B，S)-markets
……
ChapterⅥTheoryofPricinginStochasticFinancialModels.DiscreteTime
1.Europeanhedgepricingonarbitrage-freemarkets
2.Americanhedgepricingonarbitrage-freemarkets
3.Schemeofseriesoflargearbitrage-freemarketsandasymptoticarbitrage
4.Europeanoptionsonabinomial(B，S)-market
5.Americanoptionsonabinomial(B，S)-market
ChapterⅦTheoryofArbitrageinStochasticFinancialModels.ContinuousTime
1.Investmentportfolioinsemimartingalemodels
2.Semimartingalemodelswithoutopportunitiesforarbitrage.Completeness
3.Semimartingaleandmartingalemeasures
4.Arbitrage，completeness，andhedgepricingindiffusionmodelsofstock
5.Arbitrage，completeness，andhedgepricingindiffusionmodelsofbonds
ChapterⅧTheoryofPricinginStochasticFinancialModels.ContinuousTime
1.Europeanoptionsindiffusion(B，S)-stockmarkets
2.Americanoptionsindiffusion(B，S)-stoekmarkets.Caseofaninfinitetimehorizon
3.Americanoptionsindiffusion(B，S)-stockmarkets.Finitetimehorizons
4.EuropeanandAmericanoptionsinadiffusion(B，P)-bondmarket
前言
Theauthorsintentionwas：toselectandexposesubjectsthatcanbenecessaryorusefultothosein-terestedinstochasticcalculusandpricinginmodelsoffinancialmarketsoperatingunderuncertainty;
tointroducethereadertothemainconcepts，notions，andresultsofstochas-ticfinancialmathematics;
todevelopapplicationsoftheseresultstovariouskindsofcalculationsre-quiredinfinancialengineering.
Theauthorconsidereditalsoamajorprioritytoanswertherequestsofteachersoffinancialmathematicsandengineeringbymakingabiastowardsprobabilisticandstatisticalideasandthemethodsofstochasticcalculusintheanalysisofmarketr/sks.
Thesubtitle"Facts，Models，Theory"appearstobeanadequatereflectionofthetextstructureandtheauthorsstyle，whichisinlargemeasurearesultofthefeedbackwithstudentsattendinghislectures(inMoscow，Ziirich，Aarhus，...).
Forinstance，anaudienceofmathematiciansdisplayedalwaysaninterestnotonlyinthemathematicalissuesoftheTheory，butalsointheFacts，thepar-ticularitiesofrealfinancialmarkets，andthewaysinwhichtheyoperate.Thishasinducedtheauthortodevotethefirstchaptertothedescriptionofthekeyobjectsandstructurespresentonthesemarkets，toexplaintherethegoalsoffinan-cialtheoryandengineering，andtodiscusssomeissuespertainingtothehistoryofprobabilisticandstatisticalideasintheanalysisoffinancialmarkets.
Ontheotherhand，anaudienceacquaintedwith，say，securitiesmarketsandsecuritiestradingshowedconsiderableinterestinvariousclassesofstochasticpro-cessesused(orconsideredasprospective)fortheconstructionofmodelsofthe
dynamicsoffinancialindicators(prices，indexes，exchangerates，...)aridimpor-tantforcalculations(ofrisks，hedgingstrategies，rationaloptionprices，etc.).
Thisiswhatwedescribeinthesecondandthethirdchapters，devotedtosto-chasticModelsbothfordiscreteandcontinuoustime.
Theauthorbelievesthatthediscussionofstochasticprocessesinthesechapterswillbeusefultoabroadrahgeofreaders，notonlytotheonesinterestedinfinancialmathematics.
Weemphasizeherethatinthediscrete-timecase，weusuallystartinourde-scriptionoftheevolutionofstochasticsequencesfromtheirDoobdecompositionintopredictableandmartingalecomponents.Oneoftencallsthisthemartingaleapproach.Regardedfromthisstandpoint，itisonlynaturalthatmartingaletheorycanprovidefinancialmathematicsandengineeringwithusefultools.
精彩書摘
CentralpointstherearetheFirstandtheSecondfundamentalassetpricingtheorems.TheFirsttheoremstates（moreorless）thatafinancialmarketisarbitrage-freeifandonlyifthereexistsaso-calledmartingale（risk-neutral）probabilitymeasuresuchthatthe（discounted）pricesmakeupamartingalewithrespecttoit.TheSecondtheoremdescribesarbitrage-freemarketswithpropertyofcompleteness,whichensuresthatonecanbuildaninvestmentportfolioofvaluereplicatingfaithfullyanygivenpay-off.
Boththeoremsdeservethenamefundamentalfortheyassignaprecisemathe-maticalmeaningtotheeconomicnotionofanarbitrage-freemarketonthebasisof（well-developed）martingaletheory.
InthesixthandtheeighthchapterswediscusspricingbasedontheFirstandtheSecondfundamentaltheorems.Herewefollowthetraditioninthatwepaymuchattentiontothecalculationofrationalpricesandhedgingstrategiesforvariouskindsof（EuropeanorAmerican）options,whicharederivativefinancialinstru-mentswithbestdevelopedpricingtheory.Optionsprovideaperfectbasisfortheunderstandingofthegeneralprinciplesandmethodsofpricingonarbitrage-freemarkets.
Ofcourse,theauthorfacedtheproblemofthechoiceofauthoritativedataandthemodeofpresentation.
