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Comparisons on aggregate risks from two sets of heterogeneous portfolios

Yiying Zhang and Peng Zhao

Insurance: Mathematics and Economics, 2015, vol. 65, issue C, 124-135

Abstract: In this paper, we stochastically compare the aggregate risks from two heterogeneous portfolios. It is shown that under suitable conditions the more heterogeneities among aggregate risks would result in larger aggregate risks in the sense of the stochastic order. The stochastic properties of aggregate risks when the claims follow proportional hazard rates models or scale models are studied. We also provide sufficient conditions for comparing the aggregate risks arising from two sets of heterogeneous portfolios with claims having gamma distributions. In particular, the aggregate risks of portfolios from dependent samples with comonotonic dependence structures or arrangement increasing density functions are discussed. The new results established strengthen and generalize several results known in the literature including Ma (2000), Khaledi and Ahmadi (2008), Xu and Hu (2011), Xu and Balakrishnan (2011), Pan et al. (2013) and Barmalzan et al. (2015).

Keywords: Arrangement increasing; Chain majorization; Increasing convex order; Multivariate majorization; PHR model; Scale model (search for similar items in EconPapers)
Date: 2015
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Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:124-135