Cascade Sensitivity Measures

42 Pages Posted: 13 Nov 2018 Last revised: 16 Nov 2020

See all articles by Silvana M. Pesenti

Silvana M. Pesenti

University of Toronto

Pietro Millossovich

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

Andreas Tsanakas

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

Date Written: November 15, 2020

Abstract

In risk analysis, sensitivity measures quantify the extent to which the probability distribution of a model output is affected by changes (stresses) in individual random input factors. For input factors that are statistically dependent, we argue that a stress on one input should also precipitate stresses in other input factors. We introduce a novel sensitivity measure, termed cascade sensitivity, defined as a derivative of a risk measure applied on the output, in the direction of an input factor. The derivative is taken after suitably transforming the random vector of inputs, thus explicitly capturing the direct impact of the stressed input factor, as well as indirect effects via other inputs. Furthermore, alternative representations of the cascade sensitivity measure are derived, allowing us to address practical issues, such as incomplete specification of the model and high computational costs. The applicability of the methodology is illustrated through the analysis of a commercially used insurance risk model.

Keywords: Sensitivity analysis, importance measures, model uncertainty, risk measures, dependence, Rosenblatt transform

Suggested Citation

Pesenti, Silvana M. and Millossovich, Pietro and Tsanakas, Andreas, Cascade Sensitivity Measures (November 15, 2020). Available at SSRN: https://ssrn.com/abstract=3270839 or http://dx.doi.org/10.2139/ssrn.3270839

Silvana M. Pesenti (Contact Author)

University of Toronto ( email )

100 St. George Street
Toronto, Ontario M5S 3G8
Canada

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

Andreas Tsanakas

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

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

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