Bao, Zhenhua; Liu, Ye A discrete-time ruin model with dependence between interclaim arrivals and claim sizes. (English) Zbl 1419.62293 Adv. Difference Equ. 2016, Paper No. 188, 14 p. (2016). Summary: We construct a discrete-time ruin model with general premium rate and dependent setting, where the time between two occurrences depends on the previous claim size. The generating function and defective renewal equation satisfied by the Gerber-Shiu expected discounted penalty function are derived by using the roots of a generalized Lundberg’s equation. Explicit expressions for the Gerber-Shiu function are obtained with discrete \(K_{m}\)-family claim sizes and geometric thresholds. Numerical illustration is then examined. Cited in 3 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B30 Risk theory, insurance (MSC2010) Keywords:dependence; Gerber-Shiu discounted penalty function; defective renewal equation; Lundberg’s equation PDFBibTeX XMLCite \textit{Z. Bao} and \textit{Y. Liu}, Adv. Difference Equ. 2016, Paper No. 188, 14 p. (2016; Zbl 1419.62293) Full Text: DOI References: [1] Cheng, S, Gerber, HU, Shiu, ESW: Discounted probabilities and ruin theory in the compound binomial model. Insur. Math. Econ. 26, 239-250 (2000) · Zbl 1013.91063 [2] Li, S: On a class of discrete time renewal risk models. Scand. Actuar. J. 2005, 241-260 (2005) · Zbl 1142.91043 [3] Cossette, H, Landriault, D, Marceau, E: Ruin probabilities in the compound Markov binomial model. Scand. Actuar. J. 2003, 301-323 (2003) · Zbl 1092.91040 [4] Woo, JK: A generalized penalty function for a class of discrete renewal processes. Scand. Actuar. J. 2012, 130-152 (2012) · Zbl 1277.60146 [5] Liu, H, Bao, Z: On a discrete-time risk model with general income and time-dependence claims. J. Comput. Appl. Math. 260, 470-481 (2014) · Zbl 1293.91099 [6] Marceau, E: On the discrete-time compound renewal risk model with dependence. Insur. Math. Econ. 44, 245-259 (2009) · Zbl 1167.91013 [7] Landriault, D: On a generalization of the expected discounted penalty function in a discrete-time insurance risk model. Appl. Stoch. Models Bus. Ind. 24, 525-539 (2008) · Zbl 1199.91084 [8] Albrecher, H, Boxma, OJ: A ruin model with dependence between claim sizes and claim intervals. Insur. Math. Econ. 35, 245-254 (2004) · Zbl 1079.91048 [9] Li, Z, Sendova, KP: On a ruin model with both interclaim times and premiums depending on claim sizes. Scand. Actuar. J. 2013, 1-21 (2013) · Zbl 1286.91142 [10] Klimenok, V: On the modification of Rouché’s theorem for the queuing theory problems. Queueing Syst. 38, 431-434 (2001) · Zbl 1079.90523 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.