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In a quantitative model with uncertain inputs, the uncertainty of the output can be summarized by a risk measure. We propose a sensitivity analysis method based on derivatives of the output risk measure, in the direction of model inputs. This produces a global sensitivity measure, explicitly linking sensitivity and uncertainty analyses. We focus on the case of distortion risk measures, deﬁned as weighted averages of output percentiles, and prove a representation of the sensitivity measure that can be evaluated on a Monte-Carlo sample, as a weighted average of gradients over the input space. When the analytical model is unknown or hard to work with, non-parametric techniques are used for gradient estimation. This process is demonstrated through the example of a non-linear insurance loss model. Furthermore, the proposed framework is extended in order to measure sensitivity to constant model parameters, uncertain statistical parameters, and random factors driving dependence between model inputs.
|Additional Information:||This is the pre-rprint and peer-reviewed version of the article, which is published in final form at http://dx.doi.org/10.1111/risa.12434. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.|
|Uncontrolled Keywords:||Sensitivity analysis, risk measures, uncertainty analysis, aggregation, parameter uncertainty, dependence.|
|Subjects:||H Social Sciences > HG Finance|
|Divisions:||Cass Business School|
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