Comparisons on aggregate risks from two sets of heterogeneous portfolios

Zhang, Yiying; Zhao, Peng

doi:10.1016/j.insmatheco.2015.09.004

Cited by 24 publications

(13 citation statements)

References 26 publications

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“…Many well-known distributions are SAI including the multivariate versions of Dirichlet distribution, inverted Dirichlet distribution, F distribution and Pareto distribution of type I. The notion of SAI has been applied in actuarial science to model the dependence among ordered random risks; see, for instance, Hua and Cheung (2008) and Zhang and Zhao (2015). RWSAI and WSAI are introduced by Wei (2014, 2015), and have been also applied in the field of financial engineering and actuarial science; see, for example, Cai and Wei (2015) and Zhang et al (2018b).…”

Section: Stochastic Versions Of Arrangement Increasingmentioning

confidence: 99%

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Ordering Properties of Extreme Claim Amounts From Heterogeneous Portfolios

Zhang¹,

Cai²,

Zhao³

2019

ASTIN Bull.

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In the context of insurance, the smallest and largest claim amounts turn out to be crucial to insurance analysis since they provide useful information for determining annual premium. In this paper, we establish sufficient conditions for comparing extreme claim amounts arising from two sets of heterogeneous insurance portfolios according to various stochastic orders. It is firstly shown that the weak supermajorization order between the transformed vectors of occurrence probabilities implies the usual stochastic ordering between the largest claim amounts when the claim severities are weakly stochastic arrangement increasing. Secondly, sufficient conditions are established for the right-spread ordering and the convex transform ordering of the smallest claim amounts arising from heterogeneous dependent insurance portfolios with possibly different number of claims. In the setting of independent multiple-outlier claims, we study the effects of heterogeneity among sample sizes on the stochastic properties of the largest and smallest claim amounts in the sense of the hazard rate ordering and the likelihood ratio ordering. Numerical examples are provided to highlight these theoretical results as well. Not only can our results be applied in the area of actuarial science, but also they can be used in other research fields including reliability engineering and auction theory.

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Section: Stochastic Versions Of Arrangement Increasingmentioning

confidence: 99%

“…. , n. In the literature, there has been tremendous study on the aggregate claim number n i=1 I i and the aggregate claim amount n i=1 I i X i by using various stochastic orders; see, for example, Ma (2000), Denuit and Frostig (2006), Khaledi and Ahmadi (2008), , Zhang and Zhao (2015) and Zhang et al (2018b).…”

Section: Introductionmentioning

confidence: 99%

Ordering Properties of Extreme Claim Amounts From Heterogeneous Portfolios

Zhang¹,

Cai²,

Zhao³

2019

ASTIN Bull.

Self Cite

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“…Also, it is known that multivariate versions of Dirichlet distribution, inverted Dirichlet distribution, F distribution and Pareto distribution of type I are all SAI and hence RWSAI and LWSAI whenever the corresponding parameters are arrayed in the ascending order. In the literature, SAI is employed to model the dependence among ordered random risks in actuarial science; see for instance, Hua and Cheung (2008), You and Li (2014) and Zhang and Zhao (2015). LWSAI, RWSAI and WSAI were introduced by Wei (2014, 2015) and have been applied in the field of financial engineering and actuarial science to model dependent stochastic returns and risks, respectively; see for example, Cai and Wei (2015) and Li (2015, 2016).…”

Section: Stochastic Versions Of Arrangement Increasingmentioning

confidence: 99%

“…Frostig (2001) and Hu and Ruan (2004) established sufficient conditions to compare aggregate claim amount by means of the symmetric supermodular, and multivariate usual and symmetric stochastic orders (see Shaked and Shanthikumar, 2007). After that, many researchers paid their attention to comparing the aggregate claim amounts arising from two sets of heterogeneous insurance portfolios; see, for example, Khaledi and Ahmadi (2008), Barmalzan et al (2015) and Zhang and Zhao (2015). However, these results were only developed under the independent assumption on the claim occurrence probabilities, which violates the fact that the occurrences of claims may be dependent in practice.…”

Section: Introductionmentioning

confidence: 99%

On Heterogeneity in the Individual Model With Both Dependent Claim Occurrences and Severities

Zhang

Li²,

Cheung³

2018

ASTIN Bull.

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It is a common belief for actuaries that the heterogeneity of claim severities in a given insurance portfolio tends to increase its dangerousness, which results in requiring more capital for covering claims. This paper aims to investigate the effects of orderings and heterogeneity among scale parameters on the aggregate claim amount when both claim occurrence probabilities and claim severities are dependent. Under the assumption that the claim occurrence probabilities are left tail weakly stochastic arrangement increasing, the actuaries' belief is examined from two directions, i.e., claim severities are comonotonic or right tail weakly stochastic arrangement increasing. Numerical examples are provided to validate these theoretical findings. An application in assets allocation is addressed as well.

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“…. , Y n ) in two portfolios, have been discussed by many researchers in literature; see, e.g., Karlin and Novikoff (1963), Ma (2000), Frostig (2001), Hu and Ruan (2004), Denuit and Frostig (2006), Khaledi and Ahmadi (2008), Zhang and Zhao (2015), , Li and Li (2016), Barmalzan et al (2018), , Barmalzan et al (2016), Barmalzan et al (2017), Balakrishnan et al (2018) and Li and Li (2018).…”

Section: Introductionmentioning

confidence: 99%

Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

Nadeb¹,

Torabi²,

Dolati³

2020

Mathematical Inequalities &Amp; Applications

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Let X λ1 , . . . , X λn be dependent non-negative random variables and Y i = I pi X λi , i = 1, . . . , n, where I p1 , . . . , I pn are independent Bernoulli random variables independent of X λi 's, with E[I pi ] = p i , i = 1, . . . , n. In actuarial sciences, Y i corresponds to the claim amount in a portfolio of risks.In this paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters λ 1 , . . . , λ n and p 1 , . . . , p n and the variables in the other set have the parameters λ

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Comparisons on aggregate risks from two sets of heterogeneous portfolios

Cited by 24 publications

References 26 publications

Ordering Properties of Extreme Claim Amounts From Heterogeneous Portfolios

Ordering Properties of Extreme Claim Amounts From Heterogeneous Portfolios

On Heterogeneity in the Individual Model With Both Dependent Claim Occurrences and Severities

Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

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