<?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>S1409-24332018000200185</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v25i2.33608</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Modelación de poblaciones vía Cadenas de Markov Tridimensionales]]></article-title>
<article-title xml:lang="en"><![CDATA[Demographic Modeling Via 3-Dimensional Markov Chains]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Víquez]]></surname>
<given-names><![CDATA[Juan José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Víquez]]></surname>
<given-names><![CDATA[Jorge Aurelio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Campos]]></surname>
<given-names><![CDATA[Alexander]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Loría]]></surname>
<given-names><![CDATA[Jorge]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mendoza]]></surname>
<given-names><![CDATA[Luis Alfredo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<volume>25</volume>
<numero>2</numero>
<fpage>185</fpage>
<lpage>214</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332018000200185&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332018000200185&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332018000200185&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen [20] En este artículo se presenta un nuevo modelo de generación poblacional que puede ser utilizado para proyectar cantidades de personas en fondos de pensiones (tanto cotizantes como jubilados) así como trabajadores en instituciones públicas. Aunado a esto, el modelo presenta oportunidades para cuantificar los flujos derivados de estas poblaciones futuras, tales como gastos en salarios, cotizaciones, pluses salariales, aportes patronales a ahorros/pensiones, entre otros. Claramente la implementación de este modelo probabilístico será de gran utilidad dentro de la caja de herramientas actuariales, aumentando la confiabilidad de las proyecciones, así como permitiendo análisis más profundos por cuanto el desglose poblacional y financiero del modelo es extenso. Aquí se construye un modelo matemático-probabilístico que permite capturar las singularidades de las transiciones entre estados, con suficiente flexibilidad como para aplicarse a varios escenarios. Se estiman exitosamente sus primeros momentos, así como el ajuste de las probabilidades que lo alimenta. Para verificar la idoneidad del modelo propuesto, se implementa con datos reales de una institución pública, y se calcula el error de estimación, presentando niveles inferiores al 2 %.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract [24] This article presents a new model for demographic simulation which can be used to forecast and estimate the number of people in pension funds (contributors and retirees) as well as workers in a public institution. Furthermore, the model introduces opportunities to quantify the financial flows coming from future populations such as salaries, contributions, salary supplements, employer contribution to savings/pensions, among others. The implementation of this probabilistic model will be of great value in the actuarial toolbox, increasing the reliability of the estimations as well as allowing deeper demographic and financial analysis given the reach of the model. We build a mathematical and probabilistic model that allows us to capture the singularities of the transitions between states with enough flexibility that it can be applied to several scenarios. We successfully estimate its first moments, and show how to adjust the required probabilities. In order to verify the exactness of the proposed model we applied it to real data from a public institution, showing that the estimation error is below the 2 %.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[cadenas de Markov]]></kwd>
<kwd lng="es"><![CDATA[generación demográfica]]></kwd>
<kwd lng="es"><![CDATA[matemática financiera]]></kwd>
<kwd lng="en"><![CDATA[Markov chains]]></kwd>
<kwd lng="en"><![CDATA[demographic simulation]]></kwd>
<kwd lng="en"><![CDATA[financial engineering]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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