Ruin probability for the bi-seasonal discrete time risk model with dependent claims        
        
    
        Volume 6, Issue 1 (2019), pp. 133–144
            
    
                    Pub. online: 1 October 2018
                    
        Type: Research Article
            
                
            
Open Access
        
            
    
                Received
19 July 2018
                                    19 July 2018
                Revised
22 September 2018
                                    22 September 2018
                Accepted
22 September 2018
                                    22 September 2018
                Published
1 October 2018
                    1 October 2018
Abstract
The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.
            References
 Andreoli, A., Ballestra, L.V., Pacelli, G.: Computing survival probabilities based on stochastic differential models. J. Comput. Appl. Math. 277, 127–137 (2015). MR3272170. https://doi.org/10.1016/j.cam.2014.08.030
 Bao, Z., Liu, Y.: A discrete-time risk model with dependence between interclaim arrivals and claim sizes. Adv. Differ. Equ. 2016, 188 (2016). MR3521141. https://doi.org/10.1186/s13662-016-0893-4
 Bernackaitė, E., Šiaulys, J.: The finite-time ruin probability for an inhomogeneous renewal risk model. J. Ind. Manag. Optim. 13(1), 207–222 (2017). MR3576051. https://doi.org/10.3934/jimo.2016012
 Bieliauskienė, E., Šiaulys, J.: Gerber-Shiu function for the discrete inhomogeneous claim case. Int. J. Comput. Math. 89(12), 1617–1630 (2012). MR2949469. https://doi.org/10.1080/00207160.2012.693607
 Blaževičius, K., Bieliauskienė, E., Šiaulys, J.: Finite-time ruin probability in the inhomogeneous claim case. Lith. Math. J. 50, 260–270 (2010). MR2719562. https://doi.org/10.1007/s10986-010-9084-2
 Castañer, A., Claramunt, M.M., Gathy, M., Lefèvre, Cl., Mármol, M.: Ruin problems for a discrete time risk model with non-homogeneous conditions. Scand. Actuar. J. 2013(2), 83–102 (2013). MR3041119. https://doi.org/10.1080/03461238.2010.546144
 Constantinescu, C., Dai, S., Ni, W., Palmowski, Z.: Ruin probabilities with dependence on the numbers of claims within fixed time window. Risks 4, 17 (2016). https://doi.org/10.3390/risks4020017
 Damarackas, J., Šiaulys, J.: Bi-seasonal discrete time risk model. Appl. Math. Comput. 247, 930–940 (2014). MR3270895. https://doi.org/10.1016/j.amc.2014.09.040
 De Vylder, F.E., Goovaerts, M.J.: Explicit finite-time and infinite-time ruin probabilities in the continuous case. Insur. Math. Econ. 24, 155–172 (1999). MR1704808. https://doi.org/10.1016/S0167-6687(98)00049-3
 Dickson, D.C.M.: Some comments on the compound binomial model. ASTIN Bull. 24, 33–45 (1994). https://doi.org/10.2143/AST.24.1.2005079
 Dickson, D.C.M.: Insurance Risk and Ruin. Cambridge University Press (2005). MR2160707. https://doi.org/10.1017/CBO9780511624155
 Dickson, D.C.M., Waters, H.R.: Recursive calculation of survival probabilities. ASTIN Bull. 21, 199–221 (1991). https://doi.org/10.2143/AST.21.2.2005364
 Gerber, H.U.: Mathematical fun with the compound binomial process. ASTIN Bull. 18, 161–168 (1988). https://doi.org/10.2143/AST.18.2.2014949
 Gerber, H.U., Shiu, E.S.W.: On the time value of ruin. N. Am. Actuar. J. 2, 48–78 (1998). MR1988433. https://doi.org/10.1080/10920277.1998.10595671
 Grigutis, A., Korvel, A., Šiaulys, J.: Ruin probabilities of a discrete-time multi-risk model. Inf. Technol. Control 44(4), 367–379 (2015). https://doi.org/10.5755/j01.itc.44.4.8635
 Grigutis, A., Korvel, A., Šiaulys, J.: Ruin probability in the three-seasonal discrete-time risk model. Mod. Stoch. Theor. Appl. 2, 421–441 (2015). MR3456147. https://doi.org/10.15559/15-VMSTA45
 Huang, X.-F., Zhang, T., Yang, Y., Jiang, T.: Ruin probabilities in a dependent discrete-time risk model with Gamma-like tailed insurance risks. Risks 5, 14 (2017). MR3506338. https://doi.org/10.3390/risks5010014
 Joe, H.: Dependence Modeling with Copulas. Monographs on Statistics and Applied Probability, vol. 134. Chapman and Hall/CRC Press (2014). MR3328438
 Li, S., Lu, Y., Garrido, J.: A review of discrete-time risk models. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 103, 321–337 (2009). MR2582636. https://doi.org/10.1007/BF03191910
 Manstavičius, M., Leipus, R.: Bounds for the Clayton copula. Nonlinear Anal. Modell. Control 22, 248–260 (2017). MR3608075. https://doi.org/10.15388/NA.2017.2.7
 McNeil, A.J., Nešlehová, J.: Multivariate Archimedean copulas, d-monotone functions and ${l_{1}}$-norm symmetric distributions. Ann. Stat. 37, 3059–3097 (2009). MR2541455. https://doi.org/10.1214/07-AOS556
 Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer (2006). MR2197664
 Răducan, A.M., Vernic, R., Zbăganu, G.: Recursive calculation of ruin probabilities at or before claim instants for non-identically distributed claims. ASTIN Bull. 45, 421–443 (2015). MR3394025. https://doi.org/10.1017/asb.2014.30
 Răducan, A.M., Vernic, R., Zbăganu, G.: On the ruin probability for nonhomogeneous claims and arbitrary inter-claim revenues. J. Comput. Appl. Math. 290, 319–333 (2015). MR3370412. https://doi.org/10.1016/j.cam.2015.05.021
 Răducan, A.M., Vernic, R., Zbăganu, G.: On a conjecture related to the ruin probability for nonhomogeneous exponentially distributed claims. Scand. Actuar. J. 2017(5), 441–451 (2017). MR3645736. https://doi.org/10.1080/03461238.2016.1174731
 Shiu, E.S.W.: The probability of eventual ruin in the compound binomial model. ASTIN Bull. 19, 179–190 (1989). https://doi.org/10.2143/AST.19.2.2014907
 Willmot, G.E.: Ruin probabilities in the compound binomial model. Insur. Math. Econ. 12, 133–142 (1993). MR1229212. https://doi.org/10.1016/0167-6687(93)90823-8
 Zhang, T., Fang, X.-N., Liu, J., Yang, Y.: Asymptotics for the partial sums and its maximum of dependent random variables. Lithuanian Mathematical Journal 57, 142–153 (2017). MR3621877. https://doi.org/10.1007/s10986-017-9348-1