IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v34y2022i4p2350-2367.html
   My bibliography  Save this article

Robust Simulation with Likelihood-Ratio Constrained Input Uncertainty

Author

Listed:
  • Zhaolin Hu

    (School of Economics and Management, Tongji University, Shanghai 200092, China)

  • L. Jeff Hong

    (School of Management and School of Data Science, Fudan University, Shanghai 200433, China)

Abstract

To use simulation models to study the behaviors of stochastic systems, one needs to specify the distribution of the input random variables. However, specifying this distribution precisely is typically difficult and even impossible in practice. The issue is known as input uncertainty in the simulation literature, and it has been considered and studied extensively in recent years. In this paper, we model the uncertainty by an ambiguity set that is defined based on the likelihood ratio between the true (unknown) distribution and the nominal distribution (i.e., the best estimate), and develop a robust simulation (RS) approach that estimates the worst-case values of performance measures of the random simulation output when the true distribution varies in the ambiguity set. We show that the RS approach is computationally tractable, and the corresponding results reveal important information of the stochastic systems and help decision makers make better decisions.

Suggested Citation

  • Zhaolin Hu & L. Jeff Hong, 2022. "Robust Simulation with Likelihood-Ratio Constrained Input Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2350-2367, July.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:4:p:2350-2367
    DOI: 10.1287/ijoc.2022.1169
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.1169
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2022.1169?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Misspecification," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 6, pages 155-216, World Scientific Publishing Co. Pte. Ltd..
    4. Soumyadip Ghosh & Henry Lam, 2019. "Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees," Operations Research, INFORMS, vol. 67(1), pages 232-249, January.
    5. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    6. L. Jeff Hong & Zhaolin Hu & Liwei Zhang, 2014. "Conditional Value-at-Risk Approximation to Value-at-Risk Constrained Programs: A Remedy via Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 385-400, May.
    7. Stephen E. Chick, 2001. "Input Distribution Selection for Simulation Experiments: Accounting for Input Uncertainty," Operations Research, INFORMS, vol. 49(5), pages 744-758, October.
    8. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    9. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    10. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    11. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
    12. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    13. Aharon Ben-Tal & Dimitris Bertsimas & David B. Brown, 2010. "A Soft Robust Model for Optimization Under Ambiguity," Operations Research, INFORMS, vol. 58(4-part-2), pages 1220-1234, August.
    14. Henry Lam, 2018. "Sensitivity to Serial Dependency of Input Processes: A Robust Approach," Management Science, INFORMS, vol. 64(3), pages 1311-1327, March.
    15. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    16. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    17. Russell R. Barton & Barry L. Nelson & Wei Xie, 2014. "Quantifying Input Uncertainty via Simulation Confidence Intervals," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 74-87, February.
    18. Bahar Biller & Canan G. Corlu, 2011. "Accounting for Parameter Uncertainty in Large-Scale Stochastic Simulations with Correlated Inputs," Operations Research, INFORMS, vol. 59(3), pages 661-673, June.
    19. Henry Lam, 2019. "Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization," Operations Research, INFORMS, vol. 67(4), pages 1090-1105, July.
    20. Wei Xie & Barry L. Nelson & Russell R. Barton, 2014. "A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation," Operations Research, INFORMS, vol. 62(6), pages 1439-1452, December.
    21. Zhaolin Hu & Jing Cao & L. Jeff Hong, 2012. "Robust Simulation of Global Warming Policies Using the DICE Model," Management Science, INFORMS, vol. 58(12), pages 2190-2206, December.
    22. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    Full references (including those not matched with items on IDEAS)

    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. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    2. Soumyadip Ghosh & Henry Lam, 2019. "Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees," Operations Research, INFORMS, vol. 67(1), pages 232-249, January.
    3. Weiwei Fan & L. Jeff Hong & Xiaowei Zhang, 2020. "Distributionally Robust Selection of the Best," Management Science, INFORMS, vol. 66(1), pages 190-208, January.
    4. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    5. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    6. Daniel Bartl & Samuel Drapeau & Ludovic Tangpi, 2017. "Computational aspects of robust optimized certainty equivalents and option pricing," Papers 1706.10186, arXiv.org, revised Mar 2019.
    7. Detering, Nils & Packham, Natalie, 2018. "Model risk of contingent claims," IRTG 1792 Discussion Papers 2018-036, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. 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.
    9. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    10. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    11. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    12. Corlu, Canan G. & Akcay, Alp & Xie, Wei, 2020. "Stochastic simulation under input uncertainty: A Review," Operations Research Perspectives, Elsevier, vol. 7(C).
    13. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    14. Nicholas G. Hall & Daniel Zhuoyu Long & Jin Qi & Melvyn Sim, 2015. "Managing Underperformance Risk in Project Portfolio Selection," Operations Research, INFORMS, vol. 63(3), pages 660-675, June.
    15. Cohen, Asaf & Saha, Subhamay, 2021. "Asymptotic optimality of the generalized cμ rule under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 206-236.
    16. Laeven, R.J.A. & Stadje, M.A., 2011. "Entropy Coherent and Entropy Convex Measures of Risk," Discussion Paper 2011-031, Tilburg University, Center for Economic Research.
    17. Yu Feng, 2019. "Theory and Application of Model Risk Quantification," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2019.
    18. Roger J. A. Laeven & Mitja Stadje, 2013. "Entropy Coherent and Entropy Convex Measures of Risk," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 265-293, May.
    19. Li, Jing, 2018. "Essays on model uncertainty in financial models," Other publications TiSEM 202cd910-7ef1-4db4-94ae-d, Tilburg University, School of Economics and Management.
    20. Fei Sun & Jingchao Li & Jieming Zhou, 2018. "Dynamic risk measures with fluctuation of market volatility under Bochne-Lebesgue space," Papers 1806.01166, arXiv.org, revised Mar 2024.

    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:inm:orijoc:v:34:y:2022:i:4:p:2350-2367. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.