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 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 and ℳ^* have many good properties on domination problems.

Keywords

Non-negative distributions / domination / class ℳ / class ℳ^* / class [inline-graphic not available: see fulltext] / Karamata index

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