Comparisons of aggregate claim numbers and amounts: a study of heterogeneity

Yiying Zhang, Peng Zhao and Ka Chun Cheung

Scandinavian Actuarial Journal, 2019, vol. 2019, issue 4, 273-290

Abstract: In this paper, we investigate how the heterogeneity among occurrence probabilities and claim severities affects the aggregate claim numbers and aggregate claim amount for an insurance portfolio. We show that higher heterogeneity (and dependence) among occurrence probabilities results in both smaller aggregate claim numbers and aggregate claim amount in the sense of the mean residual lifetime order. We also prove that as the heterogeneity among the claims increases, the aggregate claim amount increases in the sense of the usual stochastic order when the vector of occurrence probabilities is left tail weakly stochastic arrangement increasing. These theoretical findings are applied to (i) study ordering properties of convolutions of binomial random variables, (ii) provide upper bounds for the mean residual lifetime functions of the aggregate claim numbers and amount, and (iii) compare stop-loss premiums and risk capital of different insurance portfolios.

Date: 2019
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DOI: 10.1080/03461238.2018.1557738

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