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On orderings and bounds in a generalized Sparre Andersen risk model. (English) Zbl 1274.60050
Summary: A generalization of the Gerber-Shiu function proposed by (E. C. K. Cheung et al., Scand. Actuar. J. 2010, No. 3, 185–199 (2010; Zbl 1226.60123)] is used to derive some ordering properties for certain ruin-related quantities in a Sparre Andersen type risk model. Additional bounds and/or refinements can be obtained by further assuming that the claim size and the interclaim time distributions possess certain reliability properties. Finally, numerical examples are considered to compare the exact solution to the bounds.

MSC:
60E15 Inequalities; stochastic orderings
91B30 Risk theory, insurance (MSC2010)
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