On the uncertainty of VaR of individual risk

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Value at risk (VaR) is a prevalent risk measure used in financial risk management. The calculation of VaR relies on the distribution of the potential loss position which is generally unknown in practice. In this article, we introduce a model of uncertainty for the distribution of a loss variable and investigate the effect on VaR using a worst scenario approach. The proposed model is flexible and can be applied to various types of distributions. The robust VaR and an associated worst scenario measure are identified. It is shown that the choice of the loss model is still important when there is an uncertainty model.