Servicios Personalizados
Revista
Articulo
Indicadores
- Citado por SciELO
- Accesos
Links relacionados
- Similares en SciELO
Compartir
Revista de Matemática Teoría y Aplicaciones
versión impresa ISSN 1409-2433
Rev. Mat vol.18 no.1 San José jun. 2011
Integral equations for the aggregate claim amount
Ecuaciones integrales para el monto agregado de reclamaciones
Ecuaciones integrales para el monto agregado de reclamaciones
Carlos G. Pacheco–González*
*Departamento de Matemáticas, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, México. E-Mail: cpacheco@math.cinvestav.mx
Dirección para correpondencia
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.
Ver contenido disponible en pdf
References
[1] Asmussen, S. (2008) Applied Probability and Queues. Springer, New York. [ Links ]
[2] Atkinson, K. E. (1997) The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge UK. [ Links ]
[3] Brunner, H.; Kauthen, J.P. (1989) “The numerical solution of twodimensional Volterra integral equations by collocation and iterated collocation”, IMA Journal of Numerical Analysis 9(1): 47–59. [ Links ]
[4] Cheney, W. (2001) Analysis for Applied Mathematics. Springer, New York. [ Links ]
[5] Ramsay, C. M. (1994) “On an integral equation for discounted compound–annuity distributions”, ASTIN Bulletin 19(2): 191–198. [ Links ]
[6] Rolski, T.; Schmidli, H.; Schmidt, V.; Teugels, J. (1999) Stochastic Processes for Insurance and Finance. John Wiley & Sons, New York. [ Links ]
[7] Scalas, E. (2006) “Five years of continuous-time random walks in econophysics”, in: A. Namatame, T. Kaizouji & Y. Aruka (Eds.) The Complex Networks of Economic Interactions, Lectures Notes in Economics and Mathematical Systems 567, Springer Verlag, Berlin: 3–16. [ Links ]
[8] Scalas, E.; Gorenflo, R.; Mainardi, F. (2004) “Uncoupled continuoustime random walks: Solution and limiting behavior of the master equation”, Physical Review E 69(1): 011107 [8 pages]. [ Links ]
[9] Thorin, O.; Wikstad, N. (1973) “Numerical evaluation of the ruin probabilities for a finite period” Astin Bulletin 7: 137–153. [ Links ]
[10] Whitt, W. (2002) Stochastic-Process Limits. An Introduction to Stochastic-Process Limits and Their Applications to Queues. Springer, New York. [ Links ]
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