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Sensitivity analysis with χ2-divergences

Makam, V. D., Millossovich, P. ORCID: 0000-0001-8269-7507 and Tsanakas, A. ORCID: 0000-0003-4552-5532 (2021). Sensitivity analysis with χ2-divergences. Insurance: Mathematics and Economics, 100, pp. 372-383. doi: 10.1016/j.insmatheco.2021.06.007


We introduce an approach to sensitivity analysis of quantitative risk models, for the purpose of identifying the most influential inputs. The proposed approach relies on a change of measure derived by minimising the -divergence, subject to a constraint (‘stress’) on the expectation of a chosen random variable. We obtain an explicit solution of this optimisation problem in a finite space, consistent with the use of simulation models in risk management. Subsequently, we introduce metrics that allow for a coherent assessment of reverse (i.e. stressing the output and monitoring inputs) and forward (i.e. stressing the inputs and monitoring the output) sensitivities. The proposed approach is easily applicable in practice, as it only requires a single set of simulated input/output scenarios. This is demonstrated by application on a simple insurance portfolio. Furthermore, via a simulation study, we compare the sampling performance of sensitivity metrics based on the - and the Kullback-Leibler divergence, indicating that the former can be evaluated with lower sampling error.

Publication Type: Article
Additional Information: © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license This article has been published in Insurance: Mathematics and Economics by Elsevier. DOI:
Publisher Keywords: Sensitivity analysis, -divergence, Kullback-Leibler, divergence, Simulation, Sensitivity measures, Reverse stress testing
Subjects: H Social Sciences > HB Economic Theory
H Social Sciences > HF Commerce
H Social Sciences > HG Finance
Q Science > QA Mathematics
Departments: Bayes Business School > Actuarial Science & Insurance
Date available in CRO: 12 Jul 2021 14:44
Date deposited: 12 July 2021
Date of acceptance: 25 June 2021
Date of first online publication: 2 July 2021
[img] Text - Accepted Version
This document is not freely accessible until 2 January 2023 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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