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Ordering results for individual risk model with dependent location-scale claim severities. (English) Zbl 07549071

Summary: Actuaries usually believe that the heterogeneity arising from claim severities in a given insurance portfolio tends to increase its dangerousness, which in turn creates a need to reserve more risk capital for insurer to cover total claims. In this paper, we investigate the effects of heterogeneity among occurrence probabilities and claim severities on the aggregate claim amount when the claim severities are right tail weakly stochastic arrangement increasing (RWSAI) and belong to the location-scale family. The results established here generalize those in [M. Denuit and E. Frostig, Scand. Actuar. J. 2006, No. 1, 42–66 (2006; Zbl 1142.91039)] and [Y. Zhang et al., ASTIN Bull. 48, No. 2, 817–839 (2018; Zbl 1390.91219)].

MSC:

91B16 Utility theory
91B30 Risk theory, insurance (MSC2010)
60E15 Inequalities; stochastic orderings
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