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Hypermodels in mathematical finance : modelling via infinitesimal analysis

Author: Siu-Ah Ng
Publisher: River Edge, N.J. : World Scientific, ©2003.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ng, Siu-Ah.
Hypermodels in mathematical finance.
River Edge, N.J. : World Scientific, ©2003
(DLC) 52066471
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Siu-Ah Ng
ISBN: 9812564527 9789812564528 9789810244286 9810244282 1281876909 9781281876904
OCLC Number: 228115550
Description: 1 online resource (xiii, 298 pages) : illustrations
Contents: Cover --
Preface --
Contents --
Notation and Convention --
Chapter 1 Basic Concepts and Practice in Finance --
1.1 Introducing mathematical finance --
1.2 Basic securities --
1.2.1 Stocks --
1.2.2 Bonds --
1.2.3 Others: bank accounts, currencies and commodities --
1.3 Derivative securities --
1.3.1 Options --
1.3.2 Other derivative securities --
1.4 Theory and practice --
Chapter 2 Infinitesimal Analysis and Hypermodels --
2.1 Motivations --
2.2 Hypermodels and analysis --
Chapter 3 Absence of Arbitrage --
3.1 Introduction --
3.2 Absence of arbitrage and the binary tree hypermodel --
3.2.1 A mini-model --
3.2.2 Binary tree model --
3.2.3 Binary tree hypermodel --
3.2.4 Finiteness of stock prices --
3.2.5 Risk-neutral measure for binary tree hypermodel --
3.3 Black-Scholes type PDE from virtually arbitrage-free --
3.3.1 Virtually arbitrage free --
Chapter 4 Explicit Option Pricing --
4.1 From hypermodel to PDE --
4.1.1 Barrier conditions for derivative claims --
4.1.2 Tangible price processes --
4.1.3 Differential equations in a hypermodel --
4.1.4 Black-Scholes type PDE --
4.2 Pricing options explicitly --
4.2.1 The classical Black-Scholes formula --
4.3 The barrier option --
4.4 The American option --
Chapter 5 Pricing with Binary Tree Hypermodels --
5.1 Hypermodels for the Cox-Ross-Rubinstein approach --
5.2 The CRR matrix and Examples --
Chapter 6 Further Applications --
6.1 Sensitivity analysis --
6.1.1 The Greeks --
6.1.2 Computing the Greeks from translating --
6.2 Implied volatility --
6.3 Term structure of interest rates --
Chapter 7 The Mathematics of Hypermodels --
7.1 Mathematical logic and Classical Hyperanalysis --
7.1.1 Logic and hypermodels *R --
7.1.2 Construction of *R using the compactness theorem --
7.1.3 Construction of *R using ultrapowers --
7.1.4 Some basic properties of hypermodel *R --
7.1.5 Hypermodels of R in richer languages --
7.1.6 Some examples --
7.1.7 References --
7.2 The hyperuniverse --
7.2.1 Doing mathematics in the language of set theory --
7.2.2 Hyperuniverse and the hyperextension --
7.2.3 The existence of the hyperextension --
7.2.4 Applications and examples --
7.2.5 References --
7.3 Hyperanalysis of probability --
7.3.1 The Loeb measure construction --
7.3.2 Loeb integration theory --
7.3.3 Some examples --
7.4 Hypermodels of Brownian Motion --
7.4.1 Anderson's discrete hypermodel of Brownian motion --
7.4.2 Some 650_table.seel AddXMLRootTags.pl amazon-info.seel amazonls_marc.seel archivearchivein archivecontntdmin archivein archiveinarchive archiveinarchivehtmlfooter archiveinarchivehtmlheader archiveinarchivemonthlyreport archiveinarchive-service autoconfig balancereport balancereport.template balancetrack balancetrackfile balancetrackfile.template balancetrack.template base64 bash_logger.config bash_logger.config.template bash_logger.sh bridcrosswalk bridgetformat bridwatcher bridwatcher-idebk bridwrapgoogle bridwrapmarc bridwrapmarcxml bridwraponix bridwrapsoh bsdatainnotify BundleFiles.pl cdf2marc-006.seel cdf2marc-007.seel cdf2marc-008.seel cdf2marc-leader.seel cdf2marc.seel CDF2Onix.bash cir_marc.seel cleanFiles.bash cleanlogs cleannotifylogs cleanupReports.bash codelist7.seel contntdmarchivein contributor.seel contributor_table.seel copystep countmarcrecs countrecords createaccount createReports.bash crosswalk crosswalkonix2cdf crosswalk_v1_0.wsdl curlUpload.pl dcg_marc.seel dc_marc.seel dcterms_marc.seel deapfunctions deapfunctions.template dir.properties dir.properties.template dos2unix dublincore_marc_all.seel eContent.bash eContentB.bash econtenthtmlfooter econtenthtmlheader econtentinprint econtentprint econtentprintmonthlyreport econtentprint.template edifactsweep eserials eSerials.bash eserialshtmlfooter eserialshtmlheader eserialsin eserialsmonthlyreport eSweep.bash esweep-service-startup finddups formatweblog ftpVendorLabels.pl gem_marc.seel GenericXml.class GenericXml$_main_closure1.class getbridbase getbridbase.template geteserialsharvests getformat getorderid getorderid.template google_marc.seel handofforder hostwatcher hostwatcherhtmlfooter hostwatcherhtmlheader IG_35AcqOrderImportTestRequest.xml inotify jms.properties jms.properties.template listaccounts log4j.properties logsplitter makeFiles.bash marc2cdf-006.seel marc2cdf-007.seel marc2cdf-008.seel marc2cdf-leader.seel marc2cdf.seel marc2Mods-abstract.seel marc2Mods-accessCondition.seel 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onix_decomp_template.xml onix-long4amazon.seel ONIXOrderer-1.3-standalone.jar OnixSerials2Marc.seel pass2econtent productContentType_table.seel productForm_table.seel queuewatcher quiet.properties rsyncfilewatcher rsyncloginwatcher runErrLevel runErrLevel.template runRE runRE.template runVal runVal.template schemas selectrecs slxout sweepFiles.bash tempfile toplevelnotify transferredLabelFiles.lst updatelocalmvmactiveslist upload_eSerials.bash Utilities validationnotify vdatadev vdataqa vdatatst vSerials.bash wckbindata wckbinprovider wckbsweep wcp wcpFilesweep.groovy wcpinmatching wcpinmatchinghtmlfooter wcpinmatchinghtmlheader wcpinmatching-idebk wcpinmatchingmonthlyreport wcplabels wcplabelsaging wcplabelsamples wcpmanifest wcpmanifestdg1 wcpmatching wmsacqpoimport wmsacqpoimportmonthlyreport wmsinacqpoimport wmsinacqpoimporthtmlfooter wmsinacqpoimporthtmlheader wmsinacqpoimportmonthlyreport wmsinacqpoimport-qa-service wmsinacqpoimporttestenqueue wmsinpatron wmsinpatronhtmlfooter wmsinpatronhtmlheader wmsinpatronmonthlyreport wmsreports x12sweep xmlchunker xmlcleanup xmlcleanupnew xmlcleanuptest xmlcomposition XmlCompositionRequest.xsd xmlcompositionservice xmljoiner XmlToolsLib.jar continuous hypermodels of Brownian motion --
7.4.3 Some examples --
7.5 It244; Integral and Stochastic Differential Equations --
7.5.1 Some general remarks --
7.5.2 Wiener integral and lt244; integral --
7.5.3 It244;'s lemma and the Stratonovitch integral --
7.6 Solving Stochastic differential equations --
7.7 Malliavin calculus --
7.8 White noise analysis --
7.9 Universality and homogeneity properties of hyperfinite models --
Appendix.
Responsibility: Siu-Ah Ng.

Abstract:

At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives.

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    schema:description "Cover -- Preface -- Contents -- Notation and Convention -- Chapter 1 Basic Concepts and Practice in Finance -- 1.1 Introducing mathematical finance -- 1.2 Basic securities -- 1.2.1 Stocks -- 1.2.2 Bonds -- 1.2.3 Others: bank accounts, currencies and commodities -- 1.3 Derivative securities -- 1.3.1 Options -- 1.3.2 Other derivative securities -- 1.4 Theory and practice -- Chapter 2 Infinitesimal Analysis and Hypermodels -- 2.1 Motivations -- 2.2 Hypermodels and analysis -- Chapter 3 Absence of Arbitrage -- 3.1 Introduction -- 3.2 Absence of arbitrage and the binary tree hypermodel -- 3.2.1 A mini-model -- 3.2.2 Binary tree model -- 3.2.3 Binary tree hypermodel -- 3.2.4 Finiteness of stock prices -- 3.2.5 Risk-neutral measure for binary tree hypermodel -- 3.3 Black-Scholes type PDE from virtually arbitrage-free -- 3.3.1 Virtually arbitrage free -- Chapter 4 Explicit Option Pricing -- 4.1 From hypermodel to PDE -- 4.1.1 Barrier conditions for derivative claims -- 4.1.2 Tangible price processes -- 4.1.3 Differential equations in a hypermodel -- 4.1.4 Black-Scholes type PDE -- 4.2 Pricing options explicitly -- 4.2.1 The classical Black-Scholes formula -- 4.3 The barrier option -- 4.4 The American option -- Chapter 5 Pricing with Binary Tree Hypermodels -- 5.1 Hypermodels for the Cox-Ross-Rubinstein approach -- 5.2 The CRR matrix and Examples -- Chapter 6 Further Applications -- 6.1 Sensitivity analysis -- 6.1.1 The Greeks -- 6.1.2 Computing the Greeks from translating -- 6.2 Implied volatility -- 6.3 Term structure of interest rates -- Chapter 7 The Mathematics of Hypermodels -- 7.1 Mathematical logic and Classical Hyperanalysis -- 7.1.1 Logic and hypermodels *R -- 7.1.2 Construction of *R using the compactness theorem -- 7.1.3 Construction of *R using ultrapowers -- 7.1.4 Some basic properties of hypermodel *R -- 7.1.5 Hypermodels of R in richer languages -- 7.1.6 Some examples -- 7.1.7 References -- 7.2 The hyperuniverse -- 7.2.1 Doing mathematics in the language of set theory -- 7.2.2 Hyperuniverse and the hyperextension -- 7.2.3 The existence of the hyperextension -- 7.2.4 Applications and examples -- 7.2.5 References -- 7.3 Hyperanalysis of probability -- 7.3.1 The Loeb measure construction -- 7.3.2 Loeb integration theory -- 7.3.3 Some examples -- 7.4 Hypermodels of Brownian Motion -- 7.4.1 Anderson's discrete hypermodel of Brownian motion -- 7.4.2 Some 650_table.seel AddXMLRootTags.pl amazon-info.seel amazonls_marc.seel archivearchivein archivecontntdmin archivein archiveinarchive archiveinarchivehtmlfooter archiveinarchivehtmlheader archiveinarchivemonthlyreport archiveinarchive-service autoconfig balancereport balancereport.template balancetrack balancetrackfile balancetrackfile.template balancetrack.template base64 bash_logger.config bash_logger.config.template bash_logger.sh bridcrosswalk bridgetformat bridwatcher bridwatcher-idebk bridwrapgoogle bridwrapmarc bridwrapmarcxml bridwraponix bridwrapsoh 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    schema:url <http://www.books24x7.com/marc.asp?bookid=11652> ;
    schema:url <http://ebookcentral.proquest.com/lib/warw/detail.action?docID=234370> ;
    schema:url <http://www.myilibrary.com?id=187690&ref=toc> ;
    schema:url <http://site.ebrary.com/id/10083770> ;
    schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=134085> ;
    schema:url <http://ebookcentral.proquest.com/lib/columbia/detail.action?docID=234370> ;
    schema:url <http://public.ebookcentral.proquest.com/choice/publicfullrecord.aspx?p=234370> ;
    schema:url <http://www.myilibrary.com?id=187690> ;
    schema:workExample <http://worldcat.org/isbn/9789810244286> ;
    schema:workExample <http://worldcat.org/isbn/9781281876904> ;
    schema:workExample <http://worldcat.org/isbn/9789812564528> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/228115550> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/793950006#Agent/world_scientific> # World Scientific
    a bgn:Agent ;
    schema:name "World Scientific" ;
    .

<http://experiment.worldcat.org/entity/work/data/793950006#Place/river_edge_n_j> # River Edge, N.J.
    a schema:Place ;
    schema:name "River Edge, N.J." ;
    .

<http://experiment.worldcat.org/entity/work/data/793950006#Topic/business_&_economics_investments_&_securities_general> # BUSINESS & ECONOMICS--Investments & Securities--General
    a schema:Intangible ;
    schema:name "BUSINESS & ECONOMICS--Investments & Securities--General"@en ;
    .

<http://id.loc.gov/authorities/subjects/sh2008110811> # Risk management--Mathematical models
    a schema:Intangible ;
    schema:name "Risk management--Mathematical models"@en ;
    .

<http://id.loc.gov/authorities/subjects/sh2010112455> # Securities--Mathematical models
    a schema:Intangible ;
    schema:name "Securities--Mathematical models"@en ;
    .

<http://id.loc.gov/authorities/subjects/sh85067718> # Investments--Mathematical models
    a schema:Intangible ;
    schema:name "Investments--Mathematical models"@en ;
    .

<http://id.worldcat.org/fast/1098179> # Risk management--Mathematical models
    a schema:Intangible ;
    schema:name "Risk management--Mathematical models"@en ;
    .

<http://id.worldcat.org/fast/1110768> # Securities--Mathematical models
    a schema:Intangible ;
    schema:name "Securities--Mathematical models"@en ;
    .

<http://id.worldcat.org/fast/978277> # Investments--Mathematical models
    a schema:Intangible ;
    schema:name "Investments--Mathematical models"@en ;
    .

<http://viaf.org/viaf/14459923> # Siu-Ah Ng
    a schema:Person ;
    schema:familyName "Ng" ;
    schema:givenName "Siu-Ah" ;
    schema:name "Siu-Ah Ng" ;
    .

<http://worldcat.org/entity/work/data/793950006#CreativeWork/hypermodels_in_mathematical_finance>
    a schema:CreativeWork ;
    rdfs:label "Hypermodels in mathematical finance." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/228115550> ; # Hypermodels in mathematical finance : modelling via infinitesimal analysis
    .

<http://worldcat.org/isbn/9781281876904>
    a schema:ProductModel ;
    schema:isbn "1281876909" ;
    schema:isbn "9781281876904" ;
    .

<http://worldcat.org/isbn/9789810244286>
    a schema:ProductModel ;
    schema:isbn "9810244282" ;
    schema:isbn "9789810244286" ;
    .

<http://worldcat.org/isbn/9789812564528>
    a schema:ProductModel ;
    schema:isbn "9812564527" ;
    schema:isbn "9789812564528" ;
    .

<http://www.worldcat.org/title/-/oclc/228115550>
    a genont:InformationResource, genont:ContentTypeGenericResource ;
    schema:about <http://www.worldcat.org/oclc/228115550> ; # Hypermodels in mathematical finance : modelling via infinitesimal analysis
    schema:dateModified "2018-01-05" ;
    void:inDataset <http://purl.oclc.org/dataset/WorldCat> ;
    .


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