Families of update rules for non-additive measures: Applications in pricing risks
Identifieur interne : 001793 ( Istex/Corpus ); précédent : 001792; suivant : 001794Families of update rules for non-additive measures: Applications in pricing risks
Auteurs : Virginia R. YoungSource :
- Insurance Mathematics and Economics [ 0167-6687 ] ; 1998.
Abstract
Wang et al. [Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics 21 (1997) 173–183] propose axioms for prices in an insurance market. Chateauneuf et al. [Choquet pricing for financial markets with frictions, Mathematical Finance 6 (1996) 323–330] propose similar axioms for prices in a financial market with frictions. As a result of these axioms, market prices can be represented by the Choquet integral with respect to a non-additive measure. In both insurance and financial pricing, it is important to update prices in light of newly available information. This updating can be achieved by conditioning the underlying non-additive measure. Denneberg [Conditioning (updating) non-additive measures, Annals of Operations Research 52 (1994) 21–42] studies three conditioning rules for updating non-additive measures. Two of these update rules, the Bayes' and the Dempster-Shafer, are extreme cases of a family of update rules, [Gilboa, Schmeidler, Updating ambiguous beliefs, Journal of Economic Theory 59 (1993) 33–49]. In this paper, we introduce a family of update rules more general than the one of Gilboa and Schmeidler. We also show how to embed the general and Dempster-Shafer update formulas in another family of update rules. We examine the properties of these two families of update rules and the resulting conditional prices.
Url:
DOI: 10.1016/S0167-6687(98)00017-1
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Families of update rules for non-additive measures: Applications in pricing risks</title><author><name sortKey="Young, Virginia R" sort="Young, Virginia R" uniqKey="Young V" first="Virginia R." last="Young">Virginia R. Young</name><affiliation><mods:affiliation>School of Business, University of Wisconsin - Madison, Madison, WI 53706, USA</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: vyoung@bus.wisc.edu</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:5B1983EC190CE726629E0B3BCE0D9FFB873391B8</idno><date when="1998" year="1998">1998</date><idno type="doi">10.1016/S0167-6687(98)00017-1</idno><idno type="url">https://api.istex.fr/document/5B1983EC190CE726629E0B3BCE0D9FFB873391B8/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001793</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001793</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Families of update rules for non-additive measures: Applications in pricing risks</title><author><name sortKey="Young, Virginia R" sort="Young, Virginia R" uniqKey="Young V" first="Virginia R." last="Young">Virginia R. Young</name><affiliation><mods:affiliation>School of Business, University of Wisconsin - Madison, Madison, WI 53706, USA</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: vyoung@bus.wisc.edu</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Insurance Mathematics and Economics</title><title level="j" type="abbrev">INSUMA</title><idno type="ISSN">0167-6687</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1998">1998</date><biblScope unit="volume">23</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="14">14</biblScope></imprint><idno type="ISSN">0167-6687</idno></series><idno type="istex">5B1983EC190CE726629E0B3BCE0D9FFB873391B8</idno><idno type="DOI">10.1016/S0167-6687(98)00017-1</idno><idno type="PII">S0167-6687(98)00017-1</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0167-6687</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Wang et al. [Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics 21 (1997) 173–183] propose axioms for prices in an insurance market. Chateauneuf et al. [Choquet pricing for financial markets with frictions, Mathematical Finance 6 (1996) 323–330] propose similar axioms for prices in a financial market with frictions. As a result of these axioms, market prices can be represented by the Choquet integral with respect to a non-additive measure. In both insurance and financial pricing, it is important to update prices in light of newly available information. This updating can be achieved by conditioning the underlying non-additive measure. Denneberg [Conditioning (updating) non-additive measures, Annals of Operations Research 52 (1994) 21–42] studies three conditioning rules for updating non-additive measures. Two of these update rules, the Bayes' and the Dempster-Shafer, are extreme cases of a family of update rules, [Gilboa, Schmeidler, Updating ambiguous beliefs, Journal of Economic Theory 59 (1993) 33–49]. In this paper, we introduce a family of update rules more general than the one of Gilboa and Schmeidler. We also show how to embed the general and Dempster-Shafer update formulas in another family of update rules. We examine the properties of these two families of update rules and the resulting conditional prices.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>Virginia R. Young</name><affiliations><json:string>School of Business, University of Wisconsin - Madison, Madison, WI 53706, USA</json:string><json:string>E-mail: vyoung@bus.wisc.edu</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Pricing principle</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Choquet integral</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Bayes' update rule</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Dempster-Shafer update rule</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Conditional probability</value></json:item></subject><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>Wang et al. [Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics 21 (1997) 173–183] propose axioms for prices in an insurance market. Chateauneuf et al. [Choquet pricing for financial markets with frictions, Mathematical Finance 6 (1996) 323–330] propose similar axioms for prices in a financial market with frictions. As a result of these axioms, market prices can be represented by the Choquet integral with respect to a non-additive measure. In both insurance and financial pricing, it is important to update prices in light of newly available information. This updating can be achieved by conditioning the underlying non-additive measure. Denneberg [Conditioning (updating) non-additive measures, Annals of Operations Research 52 (1994) 21–42] studies three conditioning rules for updating non-additive measures. Two of these update rules, the Bayes' and the Dempster-Shafer, are extreme cases of a family of update rules, [Gilboa, Schmeidler, Updating ambiguous beliefs, Journal of Economic Theory 59 (1993) 33–49]. In this paper, we introduce a family of update rules more general than the one of Gilboa and Schmeidler. We also show how to embed the general and Dempster-Shafer update formulas in another family of update rules. We examine the properties of these two families of update rules and the resulting conditional prices.</abstract><qualityIndicators><score>7.436</score><pdfVersion>1.2</pdfVersion><pdfPageSize>540 x 749 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>5</keywordCount><abstractCharCount>1369</abstractCharCount><pdfWordCount>6074</pdfWordCount><pdfCharCount>30382</pdfCharCount><pdfPageCount>14</pdfPageCount><abstractWordCount>203</abstractWordCount></qualityIndicators><title>Families of update rules for non-additive measures: Applications in pricing risks</title><pii><json:string>S0167-6687(98)00017-1</json:string></pii><refBibs><json:item><author><json:item><name>P. Albrecht</name></json:item></author><host><volume>22</volume><pages><last>254</last><first>247</first></pages><author></author><title>ASTIN Bulletin</title></host><title>Premium calculation without arbitrage - Discussion of Venter's paper</title></json:item><json:item><author><json:item><name>A. Chateauneuf</name></json:item><json:item><name>R. Kast</name></json:item><json:item><name>A. Lapied</name></json:item></author><host><volume>6</volume><pages><last>330</last><first>323</first></pages><author></author><title>Mathematical Finance</title></host><title>Choquet pricing for financial markets with frictions</title></json:item><json:item><author><json:item><name>D. Denneberg</name></json:item></author><host><author></author><title>16th Symposium on Operations Research</title></host><title>Preference reversal and the symmetric Choquet integral</title></json:item><json:item><author><json:item><name>D. 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Schmeidler</name></json:item></author><host><volume>57</volume><pages><last>587</last><first>571</first></pages><author></author><title>Econometrica</title></host><title>Subjective probability and expected utility without additivity</title></json:item><json:item><author><json:item><name>G.G. Venter</name></json:item></author><host><volume>21</volume><pages><last>230</last><first>223</first></pages><author></author><title>ASTIN Bulletin</title></host><title>Premium calculation implications of reinsurance without arbitrage</title></json:item><json:item><author><json:item><name>S.S. Wang</name></json:item></author><host><volume>17</volume><pages><last>54</last><first>43</first></pages><author></author><title>Insurance: Mathematics and Economics</title></host><title>Insurance pricing and increased limits ratemaking by proportional hazards transforms</title></json:item><json:item><author><json:item><name>S.S. 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Wang</name></json:item></author><host><volume>94</volume><pages><last>366</last><first>355</first></pages><author></author><title>Fuzzy Sets and Systems</title></host><title>Updating non-additive measures with fuzzy information</title></json:item><json:item><host><author></author><title>Stochastic processes and distorted probabilities</title></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><serie><volume>vol. 1</volume><pages><last>50</last><first>43</first></pages><language><json:string>unknown</json:string></language><title>The New Palgrave Dictionary of Money and Finance</title></serie><host><volume>23</volume><pii><json:string>S0167-6687(00)X0020-0</json:string></pii><pages><last>14</last><first>1</first></pages><issn><json:string>0167-6687</json:string></issn><issue>1</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Insurance Mathematics and Economics</title><publicationDate>1998</publicationDate></host><categories><wos><json:string>social science</json:string><json:string>social sciences, mathematical methods</json:string><json:string>economics</json:string><json:string>science</json:string><json:string>statistics & probability</json:string><json:string>mathematics, interdisciplinary applications</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>statistics & probability</json:string></scienceMetrix></categories><publicationDate>1998</publicationDate><copyrightDate>1998</copyrightDate><doi><json:string>10.1016/S0167-6687(98)00017-1</json:string></doi><id>5B1983EC190CE726629E0B3BCE0D9FFB873391B8</id><score>0.020511843</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/5B1983EC190CE726629E0B3BCE0D9FFB873391B8/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/5B1983EC190CE726629E0B3BCE0D9FFB873391B8/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/5B1983EC190CE726629E0B3BCE0D9FFB873391B8/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Families of update rules for non-additive measures: Applications in pricing risks</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>ELSEVIER</p></availability><date>1998</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Families of update rules for non-additive measures: Applications in pricing risks</title><author xml:id="author-1"><persName><forename type="first">Virginia R.</forename><surname>Young</surname></persName><email>vyoung@bus.wisc.edu</email><note type="biography">Tel.: +1 608 265 3494; fax: +1 608 263 3142</note><affiliation>Tel.: +1 608 265 3494; fax: +1 608 263 3142</affiliation><affiliation>School of Business, University of Wisconsin - Madison, Madison, WI 53706, USA</affiliation></author></analytic><monogr><title level="j">Insurance Mathematics and Economics</title><title level="j" type="abbrev">INSUMA</title><idno type="pISSN">0167-6687</idno><idno type="PII">S0167-6687(00)X0020-0</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1998"></date><biblScope unit="volume">23</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="14">14</biblScope></imprint></monogr><idno type="istex">5B1983EC190CE726629E0B3BCE0D9FFB873391B8</idno><idno type="DOI">10.1016/S0167-6687(98)00017-1</idno><idno type="PII">S0167-6687(98)00017-1</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1998</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Wang et al. [Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics 21 (1997) 173–183] propose axioms for prices in an insurance market. Chateauneuf et al. [Choquet pricing for financial markets with frictions, Mathematical Finance 6 (1996) 323–330] propose similar axioms for prices in a financial market with frictions. As a result of these axioms, market prices can be represented by the Choquet integral with respect to a non-additive measure. In both insurance and financial pricing, it is important to update prices in light of newly available information. This updating can be achieved by conditioning the underlying non-additive measure. Denneberg [Conditioning (updating) non-additive measures, Annals of Operations Research 52 (1994) 21–42] studies three conditioning rules for updating non-additive measures. Two of these update rules, the Bayes' and the Dempster-Shafer, are extreme cases of a family of update rules, [Gilboa, Schmeidler, Updating ambiguous beliefs, Journal of Economic Theory 59 (1993) 33–49]. In this paper, we introduce a family of update rules more general than the one of Gilboa and Schmeidler. We also show how to embed the general and Dempster-Shafer update formulas in another family of update rules. We examine the properties of these two families of update rules and the resulting conditional prices.</p></abstract><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Pricing principle</term></item><item><term>Choquet integral</term></item><item><term>Bayes' update rule</term></item><item><term>Dempster-Shafer update rule</term></item><item><term>Conditional probability</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1998">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/5B1983EC190CE726629E0B3BCE0D9FFB873391B8/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>INSUMA</jid><aid>98000171</aid><ce:pii>S0167-6687(98)00017-1</ce:pii><ce:doi>10.1016/S0167-6687(98)00017-1</ce:doi><ce:copyright type="unknown" year="1998"></ce:copyright></item-info><head><ce:title>Families of update rules for non-additive measures: Applications in pricing risks</ce:title><ce:author-group><ce:author><ce:given-name>Virginia R.</ce:given-name><ce:surname>Young</ce:surname><ce:cross-ref refid="FN1"><ce:sup>∗</ce:sup></ce:cross-ref><ce:e-address>vyoung@bus.wisc.edu</ce:e-address></ce:author><ce:affiliation><ce:textfn>School of Business, University of Wisconsin - Madison, Madison, WI 53706, USA</ce:textfn></ce:affiliation><ce:footnote id="FN1"><ce:label>∗</ce:label><ce:note-para>Tel.: +1 608 265 3494; fax: +1 608 263 3142</ce:note-para></ce:footnote></ce:author-group><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>Wang et al. [Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics 21 (1997) 173–183] propose axioms for prices in an insurance market. Chateauneuf et al. [Choquet pricing for financial markets with frictions, Mathematical Finance 6 (1996) 323–330] propose similar axioms for prices in a financial market with frictions. As a result of these axioms, market prices can be represented by the Choquet integral with respect to a non-additive measure. In both insurance and financial pricing, it is important to update prices in light of newly available information. This updating can be achieved by conditioning the underlying non-additive measure. Denneberg [Conditioning (updating) non-additive measures, Annals of Operations Research 52 (1994) 21–42] studies three conditioning rules for updating non-additive measures. Two of these update rules, the Bayes' and the Dempster-Shafer, are extreme cases of a family of update rules, [Gilboa, Schmeidler, Updating ambiguous beliefs, Journal of Economic Theory 59 (1993) 33–49]. In this paper, we introduce a family of update rules more general than the one of Gilboa and Schmeidler. We also show how to embed the general and Dempster-Shafer update formulas in another family of update rules. We examine the properties of these two families of update rules and the resulting conditional prices.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Pricing principle</ce:text></ce:keyword><ce:keyword><ce:text>Choquet integral</ce:text></ce:keyword><ce:keyword><ce:text>Bayes' update rule</ce:text></ce:keyword><ce:keyword><ce:text>Dempster-Shafer update rule</ce:text></ce:keyword><ce:keyword><ce:text>Conditional probability</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Families of update rules for non-additive measures: Applications in pricing risks</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Families of update rules for non-additive measures: Applications in pricing risks</title></titleInfo><name type="personal"><namePart type="given">Virginia R.</namePart><namePart type="family">Young</namePart><affiliation>School of Business, University of Wisconsin - Madison, Madison, WI 53706, USA</affiliation><affiliation>E-mail: vyoung@bus.wisc.edu</affiliation><description>Tel.: +1 608 265 3494; fax: +1 608 263 3142</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1998</dateIssued><copyrightDate encoding="w3cdtf">1998</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Wang et al. [Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics 21 (1997) 173–183] propose axioms for prices in an insurance market. Chateauneuf et al. [Choquet pricing for financial markets with frictions, Mathematical Finance 6 (1996) 323–330] propose similar axioms for prices in a financial market with frictions. As a result of these axioms, market prices can be represented by the Choquet integral with respect to a non-additive measure. In both insurance and financial pricing, it is important to update prices in light of newly available information. This updating can be achieved by conditioning the underlying non-additive measure. Denneberg [Conditioning (updating) non-additive measures, Annals of Operations Research 52 (1994) 21–42] studies three conditioning rules for updating non-additive measures. Two of these update rules, the Bayes' and the Dempster-Shafer, are extreme cases of a family of update rules, [Gilboa, Schmeidler, Updating ambiguous beliefs, Journal of Economic Theory 59 (1993) 33–49]. In this paper, we introduce a family of update rules more general than the one of Gilboa and Schmeidler. We also show how to embed the general and Dempster-Shafer update formulas in another family of update rules. We examine the properties of these two families of update rules and the resulting conditional prices.</abstract><subject><genre>Keywords</genre><topic>Pricing principle</topic><topic>Choquet integral</topic><topic>Bayes' update rule</topic><topic>Dempster-Shafer update rule</topic><topic>Conditional probability</topic></subject><relatedItem type="host"><titleInfo><title>Insurance Mathematics and Economics</title></titleInfo><titleInfo type="abbreviated"><title>INSUMA</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">19981031</dateIssued></originInfo><identifier type="ISSN">0167-6687</identifier><identifier type="PII">S0167-6687(00)X0020-0</identifier><part><date>19981031</date><detail type="volume"><number>23</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="issue pages"><start>1</start><end>110</end></extent><extent unit="pages"><start>1</start><end>14</end></extent></part></relatedItem><identifier type="istex">5B1983EC190CE726629E0B3BCE0D9FFB873391B8</identifier><identifier type="DOI">10.1016/S0167-6687(98)00017-1</identifier><identifier type="PII">S0167-6687(98)00017-1</identifier><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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