Abstract: xtreme losses are specially relevant in the finance and insurance sectors. Here, we analyze the tail behavior of risks and its influence on risk measures. Specifically, we examine the part of the risk value of a distortion risk measure that is attributable to extreme losses. We analyze the additive properties of tail contributions to risk values when several risks are aggregated. We show that the partial contributions are subadditive if the distortion function is concave in the tail. We examine the tail behavior for quantile-based distortion risk measures, including value-at-risk (VaR) and tail value-at-risk (TVaR). We conclude that decision makers obtain relevant information about the contribution of extreme losses to risk values and about the fraction of the diversification benefit attributable to the tails. An example is used to illustrate our results.

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