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Abstract

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.

Mathematics Subject Classification: 65C20, 65R20, 65D30.

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Received: 18 Feb 2010; Revised: 26 Aug 2010; Accepted: 10 Sep 2010