IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v10y2022i7p141-d865315.html
   My bibliography  Save this article

Reverse Sensitivity Analysis for Risk Modelling

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/10/7/141/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/10/7/141/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    2. Emanuele Borgonovo, 2017. "Value of Information," International Series in Operations Research & Management Science, in: Sensitivity Analysis, chapter 0, pages 93-100, Springer.
    3. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    4. Emanuele Borgonovo, 2017. "Global Sensitivity Analysis," International Series in Operations Research & Management Science, in: Sensitivity Analysis, chapter 0, pages 129-138, Springer.
    5. 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.
    6. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    7. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    8. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Silvana M. Pesenti, 2021. "Reverse Sensitivity Analysis for Risk Modelling," Papers 2107.01065, arXiv.org, revised May 2022.
    2. Fissler, Tobias & Pesenti, Silvana M., 2023. "Sensitivity measures based on scoring functions," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1408-1423.
    3. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    4. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
    5. Li, Haihe & Wang, Pan & Huang, Xiaoyu & Zhang, Zheng & Zhou, Changcong & Yue, Zhufeng, 2021. "Vine copula-based parametric sensitivity analysis of failure probability-based importance measure in the presence of multidimensional dependencies," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    6. Wensheng Yang & Jingtang Ma & Zhenyu Cui, 2021. "Analysis of Markov chain approximation for Asian options and occupation-time derivatives: Greeks and convergence rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 359-412, April.
    7. Silvana Pesenti & Sebastian Jaimungal, 2020. "Portfolio Optimisation within a Wasserstein Ball," Papers 2012.04500, arXiv.org, revised Jun 2022.
    8. Zdeněk Kala, 2021. "New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability," Mathematics, MDPI, vol. 9(19), pages 1-20, September.
    9. Straub, Daniel & Ehre, Max & Papaioannou, Iason, 2022. "Decision-theoretic reliability sensitivity," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    10. Borgonovo, Emanuele & Hazen, Gordon B. & Jose, Victor Richmond R. & Plischke, Elmar, 2021. "Probabilistic sensitivity measures as information value," European Journal of Operational Research, Elsevier, vol. 289(2), pages 595-610.
    11. Gómez, Fabio & Tang, Qihe & Tong, Zhiwei, 2022. "The gradient allocation principle based on the higher moment risk measure," Journal of Banking & Finance, Elsevier, vol. 143(C).
    12. Vincenzo Varriale & Antonello Cammarano & Francesca Michelino & Mauro Caputo, 2021. "Sustainable Supply Chains with Blockchain, IoT and RFID: A Simulation on Order Management," Sustainability, MDPI, vol. 13(11), pages 1-23, June.
    13. Winter, Peter, 2007. "Managerial Risk Accounting and Control – A German perspective," MPRA Paper 8185, University Library of Munich, Germany.
    14. Juan Carlos Escanciano & Zaichao Du, 2015. "Backtesting Expected Shortfall: Accounting for Tail Risk," CAEPR Working Papers 2015-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    15. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    16. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    17. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    18. Qifa Xu & Lu Chen & Cuixia Jiang & Yezheng Liu, 2022. "Forecasting expected shortfall and value at risk with a joint elicitable mixed data sampling model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 407-421, April.
    19. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    20. Björn Häckel, 2010. "Risikoadjustierte Wertbeiträge zur ex ante Entscheidungsunterstützung: Ein axiomatischer Ansatz," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 21(1), pages 81-108, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:10:y:2022:i:7:p:141-:d:865315. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.