Approximations of the ultimate ruin probability in the classical risk model using the Banach's fixed-point theorem and the continuity of the ruin probability

Jaime Martínez Sánchez; Fernando Baltazar-Larios

Kybernetika (2022)

  • Volume: 58, Issue: 2, page 254-276
  • ISSN: 0023-5954

Abstract

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In this paper, we show two applications of the Banach's Fixed-Point Theorem: first, to approximate the ultimate ruin probability in the classical risk model or Cramér-Lundberg model when claim sizes have some arbitrary continuous distribution and second, we propose an algorithm based in this theorem and some conditions to guarantee the continuity of the ruin probability with respect to the weak metric (Kantorovich). In risk theory literature, there is no methodology based in the Banach's Fixed-Point Theorem to calculate the ruin probability. Numerical results in this paper, guarantee a good approximation to the analytic solution of the ruin probability problem. Finally, we present numerical examples when claim sizes have distribution light and heavy-tailed.

How to cite

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Martínez Sánchez, Jaime, and Baltazar-Larios, Fernando. "Approximations of the ultimate ruin probability in the classical risk model using the Banach's fixed-point theorem and the continuity of the ruin probability." Kybernetika 58.2 (2022): 254-276. <http://eudml.org/doc/298883>.

@article{MartínezSánchez2022,
abstract = {In this paper, we show two applications of the Banach's Fixed-Point Theorem: first, to approximate the ultimate ruin probability in the classical risk model or Cramér-Lundberg model when claim sizes have some arbitrary continuous distribution and second, we propose an algorithm based in this theorem and some conditions to guarantee the continuity of the ruin probability with respect to the weak metric (Kantorovich). In risk theory literature, there is no methodology based in the Banach's Fixed-Point Theorem to calculate the ruin probability. Numerical results in this paper, guarantee a good approximation to the analytic solution of the ruin probability problem. Finally, we present numerical examples when claim sizes have distribution light and heavy-tailed.},
author = {Martínez Sánchez, Jaime, Baltazar-Larios, Fernando},
journal = {Kybernetika},
keywords = {Banach's Fixed-Point Theorem; classical risk model; continuity of ruin probability; probabilistic metric; ultimate ruin probability},
language = {eng},
number = {2},
pages = {254-276},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Approximations of the ultimate ruin probability in the classical risk model using the Banach's fixed-point theorem and the continuity of the ruin probability},
url = {http://eudml.org/doc/298883},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Martínez Sánchez, Jaime
AU - Baltazar-Larios, Fernando
TI - Approximations of the ultimate ruin probability in the classical risk model using the Banach's fixed-point theorem and the continuity of the ruin probability
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 2
SP - 254
EP - 276
AB - In this paper, we show two applications of the Banach's Fixed-Point Theorem: first, to approximate the ultimate ruin probability in the classical risk model or Cramér-Lundberg model when claim sizes have some arbitrary continuous distribution and second, we propose an algorithm based in this theorem and some conditions to guarantee the continuity of the ruin probability with respect to the weak metric (Kantorovich). In risk theory literature, there is no methodology based in the Banach's Fixed-Point Theorem to calculate the ruin probability. Numerical results in this paper, guarantee a good approximation to the analytic solution of the ruin probability problem. Finally, we present numerical examples when claim sizes have distribution light and heavy-tailed.
LA - eng
KW - Banach's Fixed-Point Theorem; classical risk model; continuity of ruin probability; probabilistic metric; ultimate ruin probability
UR - http://eudml.org/doc/298883
ER -

References

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