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

M. Mercè Claramunt; M. Teresa Mármol; Ramón Lacayo

SORT (2005)

  • Volume: 29, Issue: 2, page 235-248
  • ISSN: 1696-2281

Abstract

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In 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 interocurrence times of Erlangian type. We focus our analysis on the probability that the process of surplus reaches a certain level before ruin occurs, χ(u,b). Our main contribution is the generalization obtained in the computation of χ(u,b) for the case of interocurrence time between claims distributed as Erlang(2,β) and the individual claim amount as Erlang(n,γ).

How to cite

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Claramunt, M. Mercè, Mármol, M. Teresa, and Lacayo, Ramón. "On the probability of reaching a barrier in an Erlang(2) risk process.." SORT 29.2 (2005): 235-248. <http://eudml.org/doc/40476>.

@article{Claramunt2005,
abstract = {In 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 interocurrence times of Erlangian type. We focus our analysis on the probability that the process of surplus reaches a certain level before ruin occurs, χ(u,b). Our main contribution is the generalization obtained in the computation of χ(u,b) for the case of interocurrence time between claims distributed as Erlang(2,β) and the individual claim amount as Erlang(n,γ).},
author = {Claramunt, M. Mercè, Mármol, M. Teresa, Lacayo, Ramón},
journal = {SORT},
keywords = {Análisis de riesgos; Barreras; Distribución de Erlang; risk theory; Erlang distribution; upper barrier; ordinary differential equation; boundary conditions},
language = {eng},
number = {2},
pages = {235-248},
title = {On the probability of reaching a barrier in an Erlang(2) risk process.},
url = {http://eudml.org/doc/40476},
volume = {29},
year = {2005},
}

TY - JOUR
AU - Claramunt, M. Mercè
AU - Mármol, M. Teresa
AU - Lacayo, Ramón
TI - On the probability of reaching a barrier in an Erlang(2) risk process.
JO - SORT
PY - 2005
VL - 29
IS - 2
SP - 235
EP - 248
AB - In 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 interocurrence times of Erlangian type. We focus our analysis on the probability that the process of surplus reaches a certain level before ruin occurs, χ(u,b). Our main contribution is the generalization obtained in the computation of χ(u,b) for the case of interocurrence time between claims distributed as Erlang(2,β) and the individual claim amount as Erlang(n,γ).
LA - eng
KW - Análisis de riesgos; Barreras; Distribución de Erlang; risk theory; Erlang distribution; upper barrier; ordinary differential equation; boundary conditions
UR - http://eudml.org/doc/40476
ER -

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