Sensitivity Analysis Using Risk Measures

Forthcoming, Risk Analysis: An International Journal.

38 Pages Posted: 24 Nov 2013 Last revised: 16 Jun 2015

See all articles by Andreas Tsanakas

Andreas Tsanakas

Bayes Business School (formerly Cass), City, University of London

Pietro Millossovich

The Business School (formerly Cass); University of Trieste - Dipartimento di Scienze Aziendali Economiche Matematiche e Statistiche B. de Finetti

Date Written: June 9, 2014

Abstract

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.

Keywords: Sensitivity analysis, risk measures, uncertainty analysis, risk aggregation, parameter uncertainty, dependence

Suggested Citation

Tsanakas, Andreas and Millossovich, Pietro, Sensitivity Analysis Using Risk Measures (June 9, 2014). Forthcoming, Risk Analysis: An International Journal., Available at SSRN: https://ssrn.com/abstract=2358003 or http://dx.doi.org/10.2139/ssrn.2358003

Andreas Tsanakas (Contact Author)

Bayes Business School (formerly Cass), City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Pietro Millossovich

The Business School (formerly Cass) ( email )

Northampton Square
London, EC1V 0HB
United Kingdom

University of Trieste - Dipartimento di Scienze Aziendali Economiche Matematiche e Statistiche B. de Finetti ( email )

Piazzale Europa, 1
Trieste, 34127
Italy

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