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Reverse Sensitivity Analysis for Risk Modelling

Author

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  • Silvana M. Pesenti

    (Department of Statistical Sciences, University of Toronto, Toronto, ON M5S 3G3, Canada)

Abstract

We consider the problem where a modeller conducts sensitivity analysis of a model consisting of random input factors, a corresponding random output of interest, and a baseline probability measure. The modeller seeks to understand how the model (the distribution of the input factors as well as the output) changes under a stress on the output’s distribution. Specifically, for a stress on the output random variable, we derive the unique stressed distribution of the output that is closest in the Wasserstein distance to the baseline output’s distribution and satisfies the stress. We further derive the stressed model, including the stressed distribution of the inputs, which can be calculated in a numerically efficient way from a set of baseline Monte Carlo samples and which is implemented in the R package SWIM on CRAN. The proposed reverse sensitivity analysis framework is model-free and allows for stresses on the output such as (a) the mean and variance, (b) any distortion risk measure including the Value-at-Risk and Expected-Shortfall, and (c) expected utility type constraints, thus making the reverse sensitivity analysis framework suitable for risk models.

Suggested Citation

  • Silvana M. Pesenti, 2022. "Reverse Sensitivity Analysis for Risk Modelling," Risks, MDPI, vol. 10(7), pages 1-23, July.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:7:p:141-:d:865315
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    References listed on IDEAS

    as
    1. Emanuele Borgonovo, 2017. "Value of Information," International Series in Operations Research & Management Science, in: Sensitivity Analysis, chapter 0, pages 93-100, Springer.
    2. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    5. Emanuele Borgonovo, 2017. "Global Sensitivity Analysis," International Series in Operations Research & Management Science, in: Sensitivity Analysis, chapter 0, pages 129-138, Springer.
    6. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    7. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    8. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    9. Vali Asimit & Liang Peng & Ruodu Wang & Alex Yu, 2019. "An efficient approach to quantile capital allocation and sensitivity analysis," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1131-1156, October.
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    Cited by:

    1. Fissler, Tobias & Pesenti, Silvana M., 2023. "Sensitivity measures based on scoring functions," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1408-1423.
    2. Andrea Senova & Alica Tobisova & Robert Rozenberg, 2023. "New Approaches to Project Risk Assessment Utilizing the Monte Carlo Method," Sustainability, MDPI, vol. 15(2), pages 1-19, January.

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