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A Copulas-Based Approach to Modeling Dependence in Decision Trees

Author

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  • Tianyang Wang

    (College of Business, Colorado State University, Fort Collins, Colorado 80523)

  • James S. Dyer

    (McCombs School of Business, The University of Texas at Austin, Austin, Texas 78712)

Abstract

This paper presents a general framework based on copulas for modeling dependent multivariate uncertainties through the use of a decision tree. The proposed dependent decision tree model allows multiple dependent uncertainties with arbitrary marginal distributions to be represented in a decision tree with a sequence of conditional probability distributions. This general framework could be naturally applied in decision analysis and real options valuations, as well as in more general applications of dependent probability trees. While this approach to modeling dependencies can be based on several popular copula families as we illustrate, we focus on the use of the normal copula and present an efficient computational method for multivariate decision and risk analysis that can be standardized for convenient application.

Suggested Citation

  • Tianyang Wang & James S. Dyer, 2012. "A Copulas-Based Approach to Modeling Dependence in Decision Trees," Operations Research, INFORMS, vol. 60(1), pages 225-242, February.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:1:p:225-242
    DOI: 10.1287/opre.1110.1004
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    References listed on IDEAS

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    3. Trigeorgis, Lenos & Tsekrekos, Andrianos E., 2018. "Real Options in Operations Research: A Review," European Journal of Operational Research, Elsevier, vol. 270(1), pages 1-24.
    4. Tianyang Wang & James S. Dyer & Warren J. Hahn, 2017. "Sensitivity analysis of decision making under dependent uncertainties using copulas," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 117-139, November.
    5. Khakzad, Nima & Khan, Faisal & Paltrinieri, Nicola, 2014. "On the application of near accident data to risk analysis of major accidents," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 116-125.
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    8. Tianyang Wang & James S. Dyer & John C. Butler, 2016. "Modeling Correlated Discrete Uncertainties in Event Trees with Copulas," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 396-410, February.
    9. Jing Ai & Patrick L. Brockett & Tianyang Wang, 2017. "Optimal Enterprise Risk Management and Decision Making With Shared and Dependent Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1127-1169, December.
    10. Haiying Wang & Ying Yuan & Tianyang Wang, 2021. "The dynamics of cross‐boundary fire—Financial contagion between the oil and stock markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(10), pages 1655-1673, October.
    11. Yang Deng & Helen X. H. Bao & Pu Gong, 2018. "Increased Tail Dependence in Global Public Real Estate Markets," International Real Estate Review, Global Social Science Institute, vol. 21(2), pages 145-168.
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    14. Yuan, Ying & Wang, Haiying & Jin, Xiu, 2022. "Pandemic-driven financial contagion and investor behavior: Evidence from the COVID-19," International Review of Financial Analysis, Elsevier, vol. 83(C).
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    16. Simon Fritzsch & Maike Timphus & Gregor Weiss, 2021. "Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?," Papers 2109.10946, arXiv.org.

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