Geodesic
Numerical estimations of probability of the ruin in the classical model of the risk with constant interest in the case of heavy tails
Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 72-81 
E. S. Skvarnik. Numerical estimations of probability of the ruin in the classical model of the risk with constant interest in the case of heavy tails. Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 72-81. http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a8/
@article{DVMG_2004_5_1_a8,
     author = {E. S. Skvarnik},
     title = {Numerical estimations of probability of the ruin in the classical model of the risk with constant interest in the case of heavy tails},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {72--81},
     year = {2004},
     volume = {5},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a8/}
}
TY  - JOUR
AU  - E. S. Skvarnik
TI  - Numerical estimations of probability of the ruin in the classical model of the risk with constant interest in the case of heavy tails
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2004
SP  - 72
EP  - 81
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a8/
LA  - ru
ID  - DVMG_2004_5_1_a8
ER  - 
%0 Journal Article
%A E. S. Skvarnik
%T Numerical estimations of probability of the ruin in the classical model of the risk with constant interest in the case of heavy tails
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2004
%P 72-81
%V 5
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a8/
%G ru
%F DVMG_2004_5_1_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

Classical risk model under constant interest is considered. Fast algorithms of its ruin probability calculation are suggested. Large differences between accuracy numerical meanings of ruin probabiity and its asymptotic are established for mean values of initial capital.

[1] P. Embrechts, N. Veraverbeke, “Estimates for the probability of ruin with special emphasis on the possibility of large claims”, Insurance: Mathematics and Economics, 1 (1982), 55–72 | DOI | MR | Zbl

[2] S. Asmussen, “Subexponential asymptotics for stochastic processes: extremal behaviour, stationary distributions and first passage probabilities”, The Annals of Applied Probability, 8 (1998), 354–374 | DOI | MR | Zbl

[3] V. V. Kalashnikov, G. Sh. Tsitsiashvili, “Tails of waiting times and their bounds”, Queueing Systems, 32 (1999), 257–283 | DOI | MR | Zbl

[4] T. Mikosch, A. Nagaev, “Rates in approximations to ruin probabilities for heavy-tailed distributions”, Extremes, 4:1 (2001), 67–78 | DOI | MR | Zbl

[5] D. G. Konstantinides, Q. H. Tang, G. Sh. Tsitsiashvili, “Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails”, Insurance: Mathematics and Economics, 31:3 (2002), 447–460 | DOI | MR | Zbl

[6] G. Sh. Tsitsiashvili, E. S. Skvarnik, Chislennoe reshenie zadachi o srednikh znacheniyakh v klassicheskoi modeli riska, Preprint IPM DVO RAN, Vladivostok, 2001, 11 pp.