Wang, Bingjie; Yan, Jigao; Cheng, Dongya Asymptotic infinite-time ruin probabilities for a bidimensional time-dependence risk model with heavy-tailed claims. (English) Zbl 1478.91055 Japan J. Ind. Appl. Math. 39, No. 1, 177-194 (2022). Summary: The paper studies asymptotic infinite-time ruin probabilities for a bidimensional time-dependent risk model, in which two insurance companies divide between them both the premium income and the aggregate claims in different positive proportions (modeling an insurer-reinsurer scenario, where the reinsurer takes over a proportion of the insurer’s losses). In the model, the claim sizes and the inter-arrival times correspondingly form a sequence of independent and identically distributed random vectors, where each pair of the vectors follows the time-dependence structure. Under the assumption that the claim sizes have consistently varying tails, asymptotic formulas for two kinds of infinite-time ruin probabilities are derived. MSC: 91B05 Risk models (general) 62P05 Applications of statistics to actuarial sciences and financial mathematics 60K10 Applications of renewal theory (reliability, demand theory, etc.) 91G05 Actuarial mathematics Keywords:bidimensional risk model; time-dependence; insurer-reinsurer; consistently varying tails; infinite-time ruin probability PDFBibTeX XMLCite \textit{B. Wang} et al., Japan J. Ind. Appl. Math. 39, No. 1, 177--194 (2022; Zbl 1478.91055) Full Text: DOI References: [1] Albrecher, H.; Teugels, JL, Exponential behavior in the presence of dependence in risk theory, J. Appl. Probab., 43, 1, 257-273 (2006) · Zbl 1097.62110 [2] Asimit, AV; Badescu, AL, Extremes on the discounted aggregate claims in a time dependent risk model, Scand. Actuar. J., 2, 93-104 (2010) · Zbl 1224.91041 [3] Avram, F.; Palmowski, Z.; Pistorius, M., A two-dimensional ruin problem on the positive quadrant, Insur. Math. Econ., 42, 1, 227-234 (2008) · Zbl 1141.91482 [4] Badescu, AL; Cheung, ECK; Landriault, D., Dependent risk models with bivariate phase-type distributions, J. Appl. Probab., 46, 1, 113-131 (2009) · Zbl 1172.91009 [5] Badescu, AL; Cheung, ECK; Rabehasaina, L., A two-dimensional risk model with proportional reinsurance, J. Appl. Probab., 48, 3, 749-765 (2011) · Zbl 1239.91073 [6] Bingham, NH; Goldie, CM; Teugels, JL, Regular Variation (1987), Cambridge: Cambridge University Press, Cambridge [7] Boudreault, M.; Cossette, H.; Landriault, D.; Marceau, E., On a risk model with dependence between interclaim arrivals and claim sizes, Scand. Actuar. J., 5, 265-285 (2006) · Zbl 1145.91030 [8] Chen, Y.; Yuen, KC; Ng, KW, Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims, Appl. Stoch. Model. Bus. Ind., 27, 3, 290-300 (2011) · Zbl 1275.91075 [9] Cheng, D., Uniform asymptotics for the finite-time ruin probability of a generalized bidimensional risk model with Brownian perturbations, Stochastics, 93, 1, 56-71 (2021) · Zbl 1490.62314 [10] Cheng, D.; Yang, Y.; Wang, X., Asymptotic finite-time ruin probabilities in a dependent bidimensional renewal risk model with subexponential claims, Jpn. J. Ind. Appl. Math., 37, 3, 657-675 (2020) · Zbl 1460.62198 [11] Cheng, D.; Yu, C., Asymptotics for the ruin probabilities of a bidimensional renewal risk model, Dyn. Syst. Appl., 26, 1, 517-534 (2017) · Zbl 1458.62236 [12] Cheng, D.; Yu, C., Uniform asymptotics for the ruin probabilities in a bidimensional renewal risk model with strongly subexponential claims, Stochastics, 91, 5, 643-656 (2019) · Zbl 1493.62580 [13] Cheng, D.; Yu, C., Asymptotic ruin probabilities of a two-dimensional renewal risk model with dependent inter-arrival times, Commun. Stat. Theory Methods, 49, 7, 1742-1760 (2020) · Zbl 1511.91035 [14] Cossette, H.; Marceau, E.; Marri, F., On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula, Insur. Math. Econ., 43, 3, 444-455 (2008) · Zbl 1151.91565 [15] Embrechts, P.; Klüppelberg, C.; Mikosch, T., Modelling Extremal Events for Insurance and Finance (1997), Berlin: Springer, Berlin · Zbl 0873.62116 [16] Fu, KA, On joint ruin probability for a bidimensional Lévy-driven risk model with stochastic returns and heavy-tailed claims, J. Math. Anal. Appl., 442, 1, 17-30 (2016) · Zbl 1336.91047 [17] Fu, KA; Ni, C.; Chen, H., A particular bidimensional time-dependent renewal risk model with constant interest rates, Prob. Eng. Inf. Sci., 34, 2, 172-182 (2020) · Zbl 1434.60254 [18] Hu, Z.; Jiang, B., On joint ruin probabilities of a two-dimensional risk model with constant interest rate, J. Appl. Prob., 50, 2, 309-322 (2013) · Zbl 1266.91034 [19] Jiang, T.; Wang, Y.; Chen, Y.; Xu, H., Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model, Insur. Math. Econ., 64, 45-53 (2015) · Zbl 1348.91155 [20] Li, J., The infinite-time ruin probability for a bidimensional renewal risk model with constant force of interest and dependent claims, Commun. Stat. Theory Methods, 46, 4, 1959-1971 (2017) · Zbl 1360.62502 [21] Li, J., A revisit to asymptotic ruin probabilities for a bidimensional renewal risk model, Stat. Prob. Lett., 140, 23-32 (2018) · Zbl 1457.62333 [22] Li, J.; Liu, Z.; Tang, Q., On the ruin probabilities of a bidimensional perturbed risk model, Insur. Math. Econ., 41, 1, 185-195 (2007) · Zbl 1119.91056 [23] Li, J.; Tang, Q.; Wu, R., Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model, Adv. Appl. Prob., 42, 4, 1126-1146 (2010) · Zbl 1205.62061 [24] Yang, H.; Li, J., Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims, Insur. Math. Econ., 58, 185-192 (2014) · Zbl 1304.60100 [25] Yang, H.; Li, J., Asymptotic ruin probabilities for a bidimensional renewal risk model, Stochastics, 89, 5, 687-708 (2017) · Zbl 1394.60090 [26] Yang, Y.; Wang, K.; Liu, J.; Zhang, Z., Asymptotics for a bidimensional risk model with two geometric lévy price processes, J. Ind. Manage. Optim., 15, 2, 481-505 (2019) · Zbl 1438.91119 [27] Yang, Y.; Yuen, KC, Finite-time and infinite-time ruin probabilities in a two-dimensional delayed renewal risk model with Sarmanov dependent claims, J. Math. Anal. Appl., 442, 2, 600-626 (2016) · Zbl 1382.91048 This reference list is based on information provided by the publisher or from digital mathematics libraries. 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