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Ruin probability for the bi-seasonal discrete time risk model with dependent claims. (English) Zbl 1425.91231

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
91B70 Stochastic models in economics

Software:

CopulaModel
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References:

[1] Andreoli, A.; Ballestra, L. V.; Pacelli, G., Computing survival probabilities based on stochastic differential models, J. Comput. Appl. Math., 277, 127-137, (2015) · Zbl 1310.65008
[2] Bao, Z.; Liu, Y., A discrete-time risk model with dependence between interclaim arrivals and claim sizes, Adv. Differ. Equ., 2016, (2016) · Zbl 1419.62293
[3] Bernackaitė, E.; Šiaulys, J., The finite-time ruin probability for an inhomogeneous renewal risk model, J. Ind. Manag. Optim., 13, 1, 207-222, (2017) · Zbl 1369.91078
[4] Bieliauskienė, E.; Šiaulys, J., Gerber-Shiu function for the discrete inhomogeneous claim case, Int. J. Comput. Math., 89, 12, 1617-1630, (2012) · Zbl 1255.91176
[5] Blaževičius, K.; Bieliauskienė, E.; Šiaulys, J., Finite-time ruin probability in the inhomogeneous claim case, Lith. Math. J., 50, 260-270, (2010) · Zbl 1203.91111
[6] 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) · Zbl 1280.91091
[7] 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)
[8] Damarackas, J.; Šiaulys, J., Bi-seasonal discrete time risk model, Appl. Math. Comput., 247, 930-940, (2014) · Zbl 1338.91076
[9] 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) · Zbl 0963.91062
[10] Dickson, D. C.M., Some comments on the compound binomial model, ASTIN Bull., 24, 33-45, (1994)
[11] Dickson, D. C.M., Insurance Risk and Ruin, (2005), Cambridge University Press · Zbl 1060.91078
[12] Dickson, D. C.M.; Waters, H. R., Recursive calculation of survival probabilities, ASTIN Bull., 21, 199-221, (1991)
[13] Gerber, H. U., Mathematical fun with the compound binomial process, ASTIN Bull., 18, 161-168, (1988)
[14] Gerber, H. U.; Shiu, E. S.W., On the time value of ruin, N. Am. Actuar. J., 2, 48-78, (1998) · Zbl 1081.60550
[15] Grigutis, A.; Korvel, A.; Šiaulys, J., Ruin probabilities of a discrete-time multi-risk model, Inf. Technol. Control, 44, 4, 367-379, (2015)
[16] Grigutis, A.; Korvel, A.; Šiaulys, J., Ruin probability in the three-seasonal discrete-time risk model, Mod. Stoch. Theor. Appl., 2, 421-441, (2015) · Zbl 1349.91137
[17] 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)
[18] Joe, H., Dependence Modeling with Copulas, 134, (2014), Chapman and Hall/CRC Press · Zbl 1346.62001
[19] 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) · Zbl 1180.62151
[20] Manstavičius, M.; Leipus, R., Bounds for the Clayton copula, Nonlinear Anal. Modell. Control, 22, 248-260, (2017) · Zbl 1420.62230
[21] McNeil, A. J.; Nešlehová, J., Multivariate Archimedean copulas, d-monotone functions and \(l_1\)-norm symmetric distributions, Ann. Stat., 37, 3059-3097, (2009) · Zbl 1173.62044
[22] Nelsen, R. B., An Introduction to Copulas, (2006), Springer · Zbl 1152.62030
[23] 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) · Zbl 1390.91207
[24] 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) · Zbl 1319.91098
[25] 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) · Zbl 1401.91186
[26] Shiu, E. S.W., The probability of eventual ruin in the compound binomial model, ASTIN Bull., 19, 179-190, (1989)
[27] Willmot, G. E., Ruin probabilities in the compound binomial model, Insur. Math. Econ., 12, 133-142, (1993) · Zbl 0778.62099
[28] 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) · Zbl 1381.60073
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