Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran
10.22034/jsmta.2025.23011.1178
Abstract
The present paper investigates two types of perturbed integrated risk models to compute the asymptotic ruin probabilities: (i) the risk model which is perturbed by log-return rate, jump process, and Brownian motion process with dependent structure between the insurance risk and investment risk when the claim sizes are pairwise strong quasi-asymptotically independent. For this model, we assume that the heavy-tailed claim sizes and return jumps are caused by the systematic factors with an arbitrarily dependent structure; (ii) the risk model in which the underlying price process is a geometric Brownian motion, and the jump diffusion process is modeled by a dependent Affine process when the claim sizes are asymptotically independent. For both dependent models, the asymptotic ruin probabilities are obtained using mathematical approaches. Moreover, some numerical studies with Monte Carlo simulation using the Farlie-Gumbel-Morgenstern copula as the joint distribution function of claim sizes and return jumps are provided to verify the performance of asymptotic results. Some of the results show that, under the framework of regular variation with dependence structure, the asymptotic finite-time ruin probability is insensitive to the claim sizes.
Bazyari, A. (2025). Asymptotic ruin probabilities in a dependent perturbed integrated risk process with application. Journal of Statistical Modelling: Theory and Applications, 6(1), 59-82. doi: 10.22034/jsmta.2025.23011.1178
MLA
Bazyari, A. . "Asymptotic ruin probabilities in a dependent perturbed integrated risk process with application", Journal of Statistical Modelling: Theory and Applications, 6, 1, 2025, 59-82. doi: 10.22034/jsmta.2025.23011.1178
HARVARD
Bazyari, A. (2025). 'Asymptotic ruin probabilities in a dependent perturbed integrated risk process with application', Journal of Statistical Modelling: Theory and Applications, 6(1), pp. 59-82. doi: 10.22034/jsmta.2025.23011.1178
CHICAGO
A. Bazyari, "Asymptotic ruin probabilities in a dependent perturbed integrated risk process with application," Journal of Statistical Modelling: Theory and Applications, 6 1 (2025): 59-82, doi: 10.22034/jsmta.2025.23011.1178
VANCOUVER
Bazyari, A. Asymptotic ruin probabilities in a dependent perturbed integrated risk process with application. Journal of Statistical Modelling: Theory and Applications, 2025; 6(1): 59-82. doi: 10.22034/jsmta.2025.23011.1178
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