On domination problem of non-negative distributions

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 ℳ, 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