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

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

Creator:

Martínez Sánchez, Jaime and Baltazar-Larios, Fernando

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:180abfc2-0cf9-44d4-afbc-e89af9a0ad78
uuid:180abfc2-0cf9-44d4-afbc-e89af9a0ad78
doi:10.14736/kyb-2022-2-0254

Subject:

Banach's Fixed-Point Theorem, classical risk model, continuity of ruin probability, probabilistic metric, and ultimate ruin probability

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

254-276

Source:

Kybernetika | 2022 Volume:58 | Number:2

Harvested from:

CDK

Metadata only:

false