Bettina Grün (University Linz, Austria)
Key risk measures such as Value-at-Risk (VaR) and Conditional Tail Expectation (CTE) are important for capital allocation decisions as they inform actuaries and risk managers about the degree to which a line of business or a company is exposed to a particular aspect of risk. These measures are typically estimated based on the best fitting statistical model selected from a set of models considered for loss modeling. We propose two different approaches for finding this best fitting model. The first approach is based on finite mixtures where the components belong to the same parametric distribution family. The second approach uses composite models where different parametric distributions are used for the head and the tail of the distribution. In addition, we propose to estimate risk measures taking the model uncertainty risk into account and show how model averaging can be used to obtain suitable point estimates. Two popular data sets on Danish Fire and Norwegian Fire losses are used to illustrate the proposed methods.
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