<?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-00659421v2</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="2026-05-22T16:57:19+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Capacitary measures for completely monotone kernels via singular control</title>
            <author role="aut">
              <persName>
                <forename type="first">Aurélien</forename>
                <surname>Alfonsi</surname>
              </persName>
              <email type="md5">31bf894b0afbee816b93b95d40d45872</email>
              <email type="domain">enpc.fr</email>
              <idno type="idhal" notation="string">aurelien-alfonsi</idno>
              <idno type="idhal" notation="numeric">179447</idno>
              <idno type="halauthorid" notation="string">10973-179447</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-3816-6105</idno>
              <affiliation ref="#struct-51621"/>
              <affiliation ref="#struct-179801"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Alexander</forename>
                <surname>Schied</surname>
              </persName>
              <idno type="halauthorid">223059-0</idno>
              <affiliation ref="#struct-178985"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Aurélien</forename>
                <surname>Alfonsi</surname>
              </persName>
              <email type="md5">31bf894b0afbee816b93b95d40d45872</email>
              <email type="domain">enpc.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2012-01-12 17:01:48</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2012-01-19 18:04:10</date>
              <date type="whenModified">2026-02-07 05:09:16</date>
              <date type="whenReleased">2012-01-19 20:18:07</date>
              <date type="whenProduced">2013</date>
              <date type="whenEndEmbargoed">2012-01-19</date>
              <ref type="file" target="https://enpc.hal.science/hal-00659421v2/document">
                <date notBefore="2012-01-19"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://enpc.hal.science/hal-00659421v2/file/verification19wa.pdf" id="file-661531-576457">
                <date notBefore="2012-01-19"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1201.2756"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="115420">
                <persName>
                  <forename>Aurélien</forename>
                  <surname>Alfonsi</surname>
                </persName>
                <email type="md5">31bf894b0afbee816b93b95d40d45872</email>
                <email type="domain">enpc.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00659421</idno>
            <idno type="halUri">https://enpc.hal.science/hal-00659421</idno>
            <idno type="halBibtex">alfonsi:hal-00659421</idno>
            <idno type="halRefHtml">&lt;i&gt;SIAM Journal on Control and Optimization&lt;/i&gt;, 2013, 51 (2), pp.1758-1780. &lt;a target="_blank" href="https://dx.doi.org/10.1137/120862223"&gt;&amp;#x27E8;10.1137/120862223&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">SIAM Journal on Control and Optimization, 2013, 51 (2), pp.1758-1780. &amp;#x27E8;10.1137/120862223&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-661531-576457"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="CERMICS" corresp="ENPC">Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique</idno>
            <idno type="stamp" n="AO-ECONOMIE">Archives ouvertes de l'Economie</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</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="UNIV-EIFFEL">Université Gustave Eiffel</idno>
            <idno type="stamp" n="UPEM-UNIVEIFFEL">Université Paris-Est Marne-la-Vallée</idno>
            <idno type="stamp" n="INRIA-ALLEMAGNE">INRIA-ALLEMAGNE</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Capacitary measures for completely monotone kernels via singular control</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Aurélien</forename>
                    <surname>Alfonsi</surname>
                  </persName>
                  <email type="md5">31bf894b0afbee816b93b95d40d45872</email>
                  <email type="domain">enpc.fr</email>
                  <idno type="idhal" notation="string">aurelien-alfonsi</idno>
                  <idno type="idhal" notation="numeric">179447</idno>
                  <idno type="halauthorid" notation="string">10973-179447</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-3816-6105</idno>
                  <affiliation ref="#struct-51621"/>
                  <affiliation ref="#struct-179801"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Alexander</forename>
                    <surname>Schied</surname>
                  </persName>
                  <idno type="halauthorid">223059-0</idno>
                  <affiliation ref="#struct-178985"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">8477</idno>
                <idno type="issn">0363-0129</idno>
                <idno type="eissn">1095-7138</idno>
                <title level="j">SIAM Journal on Control and Optimization</title>
                <imprint>
                  <publisher>Society for Industrial and Applied Mathematics</publisher>
                  <biblScope unit="volume">51</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">1758-1780</biblScope>
                  <date type="datePub">2013</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1201.2756</idno>
              <idno type="doi">10.1137/120862223</idno>
            </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="halDomain" n="qfin.cp">Quantitative Finance [q-fin]/Computational Finance [q-fin.CP]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We give a singular control approach to the problem of minimizing an energy functional for measures with given total mass on a compact real interval, when energy is defined in terms of a completely monotone kernel. This problem occurs both in potential theory and when looking for optimal financial order execution strategies under transient price impact. In our setup, measures or order execution strategies are interpreted as singular controls, and the capacitary measure is the unique optimal control. The minimal energy, or equivalently the capacity of the underlying interval, is characterized by means of a nonstandard infinite-dimensional Riccati differential equation, which is analyzed in some detail. We then show that the capacitary measure has two Dirac components at the endpoints of the interval and a continuous Lebesgue density in between. This density can be obtained as the solution of a certain Volterra integral equation of the second kind.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-51621" status="OLD">
          <idno type="IdRef">151174822</idno>
          <idno type="ISNI">0000000403826254</idno>
          <idno type="RNSR">200320607R</idno>
          <idno type="ROR">https://ror.org/03wct8w46</idno>
          <idno type="Wikidata">Q51781803</idno>
          <orgName>Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique</orgName>
          <orgName type="acronym">CERMICS</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cermics.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-179801" status="OLD">
          <idno type="RNSR">201221215M</idno>
          <orgName>Mathematical Risk handling</orgName>
          <orgName type="acronym">MATHRISK</orgName>
          <date type="start">2012-01-01</date>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/mathrisk</ref>
          </desc>
          <listRelation>
            <relation active="#struct-86790" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-301243" type="direct"/>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-178985" status="INCOMING">
          <orgName>Department of Mathematics</orgName>
          <desc>
            <address>
              <country key="DE"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-254729" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-86790" status="OLD">
          <orgName>Inria Paris-Rocquencourt</orgName>
          <date type="end">2016-03-30</date>
          <desc>
            <address>
              <addrLine>INRIA Rocquencourt : Domaine de Voluceau, Rocquencourt B.P. 105 78153 le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris-rocquencourt</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </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-301243" status="OLD">
          <idno type="IdRef">030820499</idno>
          <idno type="ISNI">0000000115124813</idno>
          <idno type="ROR">https://ror.org/02aqt9c37</idno>
          <orgName>Université Paris-Est Marne-la-Vallée</orgName>
          <orgName type="acronym">UPEM</orgName>
          <date type="start">1991-07-22</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 boulevard Descartes - Champs-sur-Marne - 77454 Marne-la-Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-pem.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-254729" status="VALID">
          <idno type="ROR">https://ror.org/031bsb921</idno>
          <orgName>University of Mannheim = Universität Mannheim</orgName>
          <desc>
            <address>
              <addrLine>Schloss, 68131 Mannheim</addrLine>
              <country key="DE"/>
            </address>
            <ref type="url">https://www.uni-mannheim.de/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>