Title: Application of regenerative processes approach for the approximation of the ruin probability in a bivariate classical risk model with large claims

Authors: Safia Hocine; Djamil Aïssani; Aicha Bareche; Zina Benouaret

Addresses: Research Unit LaMOS, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria ' Research Unit LaMOS, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria ' Research Unit LaMOS, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria ' Research Unit LaMOS, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria

Abstract: In order to reflect more accurately the insurance company's activity, risk models that have been recently studied in the literature are becoming increasingly complex. Moreover, the ruin probability associated with these models cannot be found explicitly. Using the theory of regenerative processes, the present paper focuses on the stability analysis of a two-dimensional classical risk model with large and independent claims. The obtained stability bound is explicitly written and applied to estimate the deviation of the ruin probability under the clarified perturbation domain of the parameters governing the considered model. This proposed approach based on the theory of regenerative processes is more suitable for the stability analysis of ruin probabilities of a risk model since it takes into account large claims, unlike the strong stability method based on Markov chains. A numerical comparison between the stability bounds obtained with both approaches (regenerative process approach and Markov chains approach) is performed, based on simulation results.

Keywords: regenerative process; strong stability; Markov chain; approximation; two-dimensional risk model; ruin probability.

DOI: 10.1504/IJMOR.2023.132837

International Journal of Mathematics in Operational Research, 2023 Vol.25 No.4, pp.433 - 462

Received: 03 Oct 2021
Accepted: 19 May 2022
Published online: 11 Aug 2023 *

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