On domination problem of non-negative distributions

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 , 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  and ℳ* have many good properties on domination problems.

Keywords

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