On the probability of reaching a barrier in an Erlang(2) risk process

• Autores: María Teresa Mármol, M. Mercè Claramunt Bielsa , Ramón Lacayo
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 29, Nº. 2, 2005, págs. 235-248
• Idioma: inglés
• Títulos paralelos:
  • Sobre la probabilidad de alcanzar una barrera en un proceso de riesgo Erlang(2).
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• Dialnet Métricas: 1 Cita
• Resumen

  • HolaIn this paper the process of aggregated claims in a non-life insurance portfolio as defined in the classical model of risk theory is modified. The Compound Poisson process is replaced with a more general renewal risk process with interoccurrence times of Erlangian type. We focus our analysis on the probability that the process of surplus reaches a certain level before ruin occurs, ¿Ô(u,b). Our main contribution is the generalization obtained in the computation of ¿Ô(u,b) for the case of interoccurrence time between claims distributed as Erlang(2, ¿À) and the individual claim amount as Erlang (n, ¿Á).

    MSC: 91B30, 62P05 Keywords: risk theory, Erlang distribution, upper barrier, ordinary differential equation, boundary conditions HolaEn aquest article es modifica el proc¿Les de reclamacions agregades d¿funa cartera d¿fassegurances de no-vida en el model cl`assic de la teoria de risc. El proc¿Les de Poisson compost ¿Les reemplac¿Cat per un proc¿Les de renaixement de risc m¿Les general amb temps d¿finter-ocurr`encia de tipus erlangi`a. Concentrem la nostra an`alisi en la probabilitat que el proc¿Les de sobrepassar assoleixi cert nivell abans d¿farribar a ru¿N.na, ¿Ô(u,b). La nostra principal contribuci¿Lo ¿Les la generalitzaci¿Lo obtinguda en el c`alcul d¿f¿Ô(u,b) per al cas de temps d¿finter-ocurr`encia entre reclamacions distribu¿N.des com Erlang (2, ¿À) i les quantitats de reclamacions individuals com Erlang (n, ¿Á).

    Paraules clau: teoria del risc, distribuci¿Lo d¿fErlang, barreres superiors, equacions diferencials ordin`aries, condicions frontera

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