In the context of insurance mathematics, we study the renewal properties of the so-called aggregate claim amount for the non-discounted and the discounted case. For these models, we set integral equations for the distribution function. Additionally we mention how the integral equation may be used to find an approximation of the distribution.
Keywords: aggregate claim amount, Volterra integral equation, discounted process.
Resumen
En el ámbito de matemáticas actuariales, estudiamos las propiedades de renovación del llamado monto agregado de reclamaciones en los casos no-descontado y descontado. Se establecen ecuaciones integrales para la función de distribución de estos modelos. Adicionalmente mencionamos como usar estas ecuaciones integrales para encontrar aproximaciones numéricas de la distribución. ]]>
Palabras clave: monto agregado de reclamaciones, ecuación integral de Volterra, proceso de descuento.
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Correspondencia a: Carlos G. Pacheco–González. Departamento de Matemáticas, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, México. E-Mail: cpacheco@math.cinvestav.mx
Received: 18 Feb 2010; Revised: 26 Aug 2010; Accepted: 10 Sep 2010