<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332022000200239</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v29i2.47938</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Estimación máxima verosimilitud de la probabilidad de ruina en el modelo de riesgo clásico con reclamaciones exponenciales]]></article-title>
<article-title xml:lang="en"><![CDATA[Maximum likelihood estimation of ruin probability in the classical risk model with exponential claims]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Guerrero-Lara]]></surname>
<given-names><![CDATA[Ernesto A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[López-Flores]]></surname>
<given-names><![CDATA[Jesús E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pantí-Trejo]]></surname>
<given-names><![CDATA[Henry G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Yucatán Facultad de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Yucatán Facultad de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Autónoma de Yucatán Facultad de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>29</volume>
<numero>2</numero>
<fpage>239</fpage>
<lpage>260</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332022000200239&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332022000200239&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332022000200239&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Se calculan los estimadores de máxima verosimilitud para los paráme- tros que definen al proceso de Poisson compuesto en el proceso de riesgo clásico con reclamaciones exponenciales. Se prueba consistencia y nor- malidad asintótica de los estimadores obtenidos. Finalmente, con ayuda de la propiedad de invarianza de los estimadores de máxima verosimili- tud, la normalidad asintótica y el método delta, se realiza una estimación puntual y por intervalos de la probabilidad de ruina.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Maximum likelihood estimators are calculated for the parameters that define the compound Poisson process in the classical risk process with exponential claims. It is proved consistency and asymptotic normality for estimators obtained. Finally, with the help of invariance property of the maximum likelihood estimators, asymptotic normality and delta method, point and interval estimation of the ruin probability is performed.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[estimación máxima verosimilitud]]></kwd>
<kwd lng="es"><![CDATA[probabilidad de ruina]]></kwd>
<kwd lng="es"><![CDATA[modelo clásico de ruina]]></kwd>
<kwd lng="es"><![CDATA[método delta.]]></kwd>
<kwd lng="en"><![CDATA[ruin probability]]></kwd>
<kwd lng="en"><![CDATA[maximum likelihood estimation]]></kwd>
<kwd lng="en"><![CDATA[classical ruin model]]></kwd>
<kwd lng="en"><![CDATA[delta method.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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