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Sensitivity analysis using risk measures

Tsanakas, A. & Millossovich, P. (2016). Sensitivity analysis using risk measures. Risk Analysis: an international journal, 36(1), pp. 30-48. doi: 10.1111/risa.12434


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.

Publication Type: Article
Additional Information: This is the pre-rprint and peer-reviewed version of the article, which is published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Publisher Keywords: Sensitivity analysis, risk measures, uncertainty analysis, aggregation, parameter uncertainty, dependence.
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School
SWORD Depositor:
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