<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00817179</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-25T01:04:54+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">An Explicit Martingale Version of Brenier's Theorem</title>
            <author role="aut">
              <persName>
                <forename type="first">Pierre</forename>
                <surname>Henry-Labordere</surname>
              </persName>
              <idno type="halauthorid">104441-0</idno>
              <affiliation ref="#struct-10234"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Nizar</forename>
                <surname>Touzi</surname>
              </persName>
              <email type="md5">573c3b814f5294fb51ddb969ebfc41bd</email>
              <email type="domain">polytechnique.edu</email>
              <idno type="idhal" notation="numeric">858649</idno>
              <idno type="halauthorid" notation="string">99556-858649</idno>
              <affiliation ref="#struct-89626"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Nizar</forename>
                <surname>Touzi</surname>
              </persName>
              <email type="md5">573c3b814f5294fb51ddb969ebfc41bd</email>
              <email type="domain">polytechnique.edu</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-04-24 06:49:22</date>
              <date type="whenModified">2025-09-02 16:02:00</date>
              <date type="whenReleased">2013-07-30 10:07:50</date>
              <date type="whenProduced">2013-04-24</date>
              <date type="whenEndEmbargoed">2013-04-24</date>
              <ref type="file" target="https://inria.hal.science/hal-00817179v1/document">
                <date notBefore="2013-04-24"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/hal-00817179v1/file/MartingaleBrenier-discret.pdf" id="file-817179-200667">
                <date notBefore="2013-04-24"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="182860">
                <persName>
                  <forename>Nizar</forename>
                  <surname>Touzi</surname>
                </persName>
                <email type="md5">573c3b814f5294fb51ddb969ebfc41bd</email>
                <email type="domain">polytechnique.edu</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00817179</idno>
            <idno type="halUri">https://inria.hal.science/hal-00817179</idno>
            <idno type="halBibtex">henrylabordere:hal-00817179</idno>
            <idno type="halRefHtml">2013</idno>
            <idno type="halRef">2013</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-817179-200667"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
            <idno type="stamp" n="IP-PARIS-MATHEMATIQUES">IP Paris Département de Mathématiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">An Explicit Martingale Version of Brenier's Theorem</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre</forename>
                    <surname>Henry-Labordere</surname>
                  </persName>
                  <idno type="halauthorid">104441-0</idno>
                  <affiliation ref="#struct-10234"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Nizar</forename>
                    <surname>Touzi</surname>
                  </persName>
                  <email type="md5">573c3b814f5294fb51ddb969ebfc41bd</email>
                  <email type="domain">polytechnique.edu</email>
                  <idno type="idhal" notation="numeric">858649</idno>
                  <idno type="halauthorid" notation="string">99556-858649</idno>
                  <affiliation ref="#struct-89626"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry-LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present martingale version. We provide the explicit martingale optimal transference plans for a remarkable class of coupling functions corresponding to the lower and upper bounds. These explicit extremal probability measures coincide with the unique left and right monotone martingale transference plans, which were introduced in \cite{BeiglbockJuillet} by suitable adaptation of the notion of cyclic monotonicity. Instead, our approach relies heavily on the (weak) duality result stated in \cite{BeiglbockHenry-LaborderePenkner}, and provides, as a by-product, an explicit expression for the corresponding optimal semi-static hedging strategies. We finally provide an extension to the multiple marginals case.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-10234" status="INCOMING">
          <orgName>Equity Derivatives Research Societe Generale</orgName>
          <orgName type="acronym">SOCIETE GENERALE</orgName>
          <desc>
            <address>
              <addrLine>Tour Société Générale 17 cours Valmy 92972 Paris La Défense Cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-305038" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-305038" status="INCOMING">
          <orgName>Société Générale</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>