De Vylder type approximation of the ruin probability for the insurer-reinsurer model

Krzysztof Burnecki, Marek A. Teuerle, and Aleksandra Wilkowska. "De Vylder type approximation of the ruin probability for the insurer-reinsurer model." Mathematica Applicanda 47.1 (2019): null. <http://eudml.org/doc/295481>.

@article{KrzysztofBurnecki2019,
abstract = {In this article we introduce a De Vylder type of approximation of the ruin probability for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. Such a process is usually associated with the insurer-reinsurer model. Applying De Vylder's idea to the risk process we obtain an approximation of the ruin probability for an arbitrary claim amount distribution only assuming that the third moment exists. We check the performance of the approximation by means of the Monte Carlo simulations studying several typical claim amount distributions. All results show that the proposed approximation yields very small relative errors. Finally, we illustrate the approximation by considering real-world loss data obtained from a Polish insurance company.},
author = {Krzysztof Burnecki, Marek A. Teuerle, Aleksandra Wilkowska},
journal = {Mathematica Applicanda},
keywords = {ruin probability, two-dimensional risk process, De Vylder approximation.},
language = {eng},
number = {1},
pages = {null},
title = {De Vylder type approximation of the ruin probability for the insurer-reinsurer model},
url = {http://eudml.org/doc/295481},
volume = {47},
year = {2019},
}

TY - JOUR
AU - Krzysztof Burnecki
AU - Marek A. Teuerle
AU - Aleksandra Wilkowska
TI - De Vylder type approximation of the ruin probability for the insurer-reinsurer model
JO - Mathematica Applicanda
PY - 2019
VL - 47
IS - 1
SP - null
AB - In this article we introduce a De Vylder type of approximation of the ruin probability for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. Such a process is usually associated with the insurer-reinsurer model. Applying De Vylder's idea to the risk process we obtain an approximation of the ruin probability for an arbitrary claim amount distribution only assuming that the third moment exists. We check the performance of the approximation by means of the Monte Carlo simulations studying several typical claim amount distributions. All results show that the proposed approximation yields very small relative errors. Finally, we illustrate the approximation by considering real-world loss data obtained from a Polish insurance company.
LA - eng
KW - ruin probability, two-dimensional risk process, De Vylder approximation.
UR - http://eudml.org/doc/295481
ER -