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A nonlinear certainty equivalent approximation method for dynamic stochastic problems

Author

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  • Yongyang Cai
  • Kenneth Judd
  • Jevgenijs Steinbuks

Abstract

This paper introduces a nonlinear certainty‐equivalent approximation method for dynamic stochastic problems. We first introduce a novel, stable, and efficient method for computing the decision rules in deterministic dynamic economic problems. We use the results as nonlinear and global certainty‐equivalent approximations for solutions to stochastic problems, and compare their accuracy to the common linear and local certainty‐equivalent methods. Our examples demonstrate that this method can be applied to solve high‐dimensional problems with up to 400 state variables with acceptable accuracy. This method can also be applied to solve problems with inequality constraints. These features make the nonlinear certainty‐equivalent approximation method suitable for solving complex economic problems, where other algorithms, such as log‐linearization, fail to produce a valid global approximation or are far less tractable.

Suggested Citation

  • Yongyang Cai & Kenneth Judd & Jevgenijs Steinbuks, 2017. "A nonlinear certainty equivalent approximation method for dynamic stochastic problems," Quantitative Economics, Econometric Society, vol. 8(1), pages 117-147, March.
    • Handle: RePEc:wly:quante:v:8:y:2017:i:1:p:117-147
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    Cited by:

    1. Dou, Shi-quan & Liu, Jiang-yi & Xiao, Jian-zhong & Pan, Wen, 2020. "Economic feasibility valuing of deep mineral resources based on risk analysis: Songtao manganese ore - China case study," Resources Policy, Elsevier, vol. 66(C).
    2. Haktanır, Elif & Kahraman, Cengiz, 2023. "Intuitionistic fuzzy risk adjusted discount rate and certainty equivalent methods for risky projects," International Journal of Production Economics, Elsevier, vol. 257(C).
    3. Yongyang Cai & Kenneth L. Judd, 2023. "A simple but powerful simulated certainty equivalent approximation method for dynamic stochastic problems," Quantitative Economics, Econometric Society, vol. 14(2), pages 651-687, May.
    4. Yongyang Cai, 2020. "The Role of Uncertainty in Controlling Climate Change," Papers 2003.01615, arXiv.org, revised Oct 2020.
    5. Duong Ngotran, 2016. "The E-Monetary Theory," 2016 Papers png175, Job Market Papers.
    6. Aldrich Eric Mark & Kung Howard, 2021. "Computational Methods for Production-Based Asset Pricing Models with Recursive Utility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-26, February.
    7. Jan Bruha, 2015. "Dynamics of Linear Forward-looking Structural Macroeconomic Models at the Zero Lower Bound: Do Solution Techniques Matter?," Working Papers 2015/13, Czech National Bank, Research and Statistics Department.
    8. Cai,Yongyang & Steinbuks,Jevgenijs & Judd,Kenneth L. & Jaegermeyr,Jonas & Hertel,Thomas W., 2020. "Modeling Uncertainty in Large Natural Resource Allocation Problems," Policy Research Working Paper Series 9159, The World Bank.
    9. Wonjun Chang & Michael C. Ferris & Youngdae Kim & Thomas F. Rutherford, 2020. "Solving Stochastic Dynamic Programming Problems: A Mixed Complementarity Approach," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 925-955, March.
    10. Golub, Alla & Cai, Yongyang & Hertel, Thomas & Steinbuks, Jevgenijs, 2015. "Energy Price Uncertainty and Global Land Use," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205406, Agricultural and Applied Economics Association.
    11. Inna Tsener, 2020. "A geometric programming approach to dynamic economic models," Economics Bulletin, AccessEcon, vol. 40(2), pages 1068-1074.
    12. Dennis, Richard, 2024. "Using a hyperbolic cross to solve non-linear macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    13. Yongyang Cai, 2025. "Modeling Uncertainty in Integrated Assessment Models," Papers 2511.00378, arXiv.org.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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