On domination problem of non-negative distributions

doi:10.1007/s11464-009-0040-6

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Front. Math. China ›› 2009, Vol. 4 ›› Issue (4) : 681-696. DOI: 10.1007/s11464-009-0040-6

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On domination problem of non-negative distributions

Zishan SU,Chun SU,Zhishui HU,Jie LIU,

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Abstract

The domination relationship between non-negative distributions is an important question in applied probability. It has important applications in the fields of finance, insurance and risk theory. In this paper, based on class "Graphic"

, we find the sufficient condition of dominating all light-tailed distributions and also discuss its necessity. Almost all heavy-tailed distributions often used in risk theory satisfy this condition. We also consider the domination problem between heavy-tailed distributions, and show that classes "Graphic"

 and "Graphic"

ℳ* have many good properties on domination problems.

Keywords

[img]Non-negative distributions / domination / class / class ℳ / class  / Karamata index

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Zishan SU, Chun SU, Zhishui HU, Jie LIU,. On domination problem of non-negative distributions. Front. Math. China, 2009, 4(4): 681‒696 https://doi.org/10.1007/s11464-009-0040-6