1Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland and Institute of Power Systems Automation Wystawowa 1 51-618 Wrocław, Poland 2Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland
Applicationes Mathematicae, Tome 32 (2005) no. 2, pp. 155-176
We compare 12 different approximations of ruin probability in infinite time studying typical light- and
heavy-tailed claim size distributions, namely exponential, mixture of exponentials, gamma, lognormal, Weibull, loggamma, Pareto and Burr. We show
that approximation based on the Pollaczek–Khinchin formula gives most accurate results, in fact it can be chosen as a reference method. We
also introduce a promising modification to the De Vylder approximation.
Keywords:
compare different approximations ruin probability infinite time studying typical light heavy tailed claim size distributions namely exponential mixture exponentials gamma lognormal weibull loggamma pareto burr approximation based pollaczek khinchin formula gives accurate results chosen reference method introduce promising modification vylder approximation
Affiliations des auteurs :
Krzysztof Burnecki
1
;
Paweł Miśta
2
;
Aleksander Weron
2
1
Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland and Institute of Power Systems Automation Wystawowa 1 51-618 Wrocław, Poland
2
Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland
@article{10_4064_am32_2_4,
author = {Krzysztof Burnecki and Pawe{\l} Mi\'sta and Aleksander Weron},
title = {What is the best approximation of ruin probability in infinite time?},
journal = {Applicationes Mathematicae},
pages = {155--176},
year = {2005},
volume = {32},
number = {2},
doi = {10.4064/am32-2-4},
zbl = {1075.62093},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am32-2-4/}
}
TY - JOUR
AU - Krzysztof Burnecki
AU - Paweł Miśta
AU - Aleksander Weron
TI - What is the best approximation of ruin probability in infinite time?
JO - Applicationes Mathematicae
PY - 2005
SP - 155
EP - 176
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/am32-2-4/
DO - 10.4064/am32-2-4
LA - en
ID - 10_4064_am32_2_4
ER -
%0 Journal Article
%A Krzysztof Burnecki
%A Paweł Miśta
%A Aleksander Weron
%T What is the best approximation of ruin probability in infinite time?
%J Applicationes Mathematicae
%D 2005
%P 155-176
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/am32-2-4/
%R 10.4064/am32-2-4
%G en
%F 10_4064_am32_2_4
Krzysztof Burnecki; Paweł Miśta; Aleksander Weron. What is the best approximation of ruin probability in infinite time?. Applicationes Mathematicae, Tome 32 (2005) no. 2, pp. 155-176. doi: 10.4064/am32-2-4
