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

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.