Bieliauskienė, Eugenija; Šiaulys, Jonas Gerber-Shiu function for the discrete inhomogeneous claim case. (English) Zbl 1255.91176 Int. J. Comput. Math. 89, No. 12, 1617-1630 (2012). Summary: The discrete time risk model with non-identically distributed claims is investigated. Finite and infinite time recursive Gerber–Shiu functions are considered and the algorithm of calculation guidelines is written. Examples of ruin probability and Gerber–Shiu function behaviour are shown. Cited in 5 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 60G50 Sums of independent random variables; random walks Keywords:discrete time risk model; Gerber-Shiu function; ruin probability; recursive formula; inhomogeneous claims PDFBibTeX XMLCite \textit{E. Bieliauskienė} and \textit{J. Šiaulys}, Int. J. Comput. Math. 89, No. 12, 1617--1630 (2012; Zbl 1255.91176) Full Text: DOI References: [1] DOI: 10.1016/j.amc.2005.11.106 · Zbl 1158.60374 · doi:10.1016/j.amc.2005.11.106 [2] Bieliauskien\.e E., Liet. Mat. Rink. LMD darbai. 51 pp 352– (2010) [3] DOI: 10.1007/s10986-010-9084-2 · Zbl 1203.91111 · doi:10.1007/s10986-010-9084-2 [4] DOI: 10.1016/0167-6687(88)90089-3 · Zbl 0629.62101 · doi:10.1016/0167-6687(88)90089-3 [5] DOI: 10.2143/AST.24.1.2005079 · doi:10.2143/AST.24.1.2005079 [6] DOI: 10.1017/S135732170000057X · doi:10.1017/S135732170000057X [7] DOI: 10.1017/CBO9780511624155 · doi:10.1017/CBO9780511624155 [8] DOI: 10.2143/AST.21.2.2005364 · doi:10.2143/AST.21.2.2005364 [9] DOI: 10.2143/AST.18.2.2014949 · doi:10.2143/AST.18.2.2014949 [10] Gerber H. U., N. Am. Actuar. J. 2 pp 48– (1998) · Zbl 1081.60550 · doi:10.1080/10920277.1998.10595671 [11] DOI: 10.1214/08-PS134 · Zbl 1189.91077 · doi:10.1214/08-PS134 [12] DOI: 10.2143/AST.19.2.2014907 · doi:10.2143/AST.19.2.2014907 [13] DOI: 10.1023/B:JOTH.0000036319.21285.22 · Zbl 1065.91040 · doi:10.1023/B:JOTH.0000036319.21285.22 [14] DOI: 10.1016/0167-6687(93)90823-8 · Zbl 0778.62099 · doi:10.1016/0167-6687(93)90823-8 [15] DOI: 10.1002/asmb.752 · Zbl 1224.91097 · doi:10.1002/asmb.752 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.