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Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems

Author

Listed:
  • Lucas Merabet

    (METRON)

  • Bernardo Freitas Paulo Costa

    (Getulio Vargas Foundation
    Federal University of Rio de Janeiro)

  • Vincent Leclere

    (Ecole des Ponts)

Abstract

Risk-averse multistage problems and their applications are gaining interest in various fields of applications. Under convexity assumptions, the resolution of these problems can be done with trajectory following dynamic programming algorithms like Stochastic Dual Dynamic Programming (SDDP) to access a deterministic lower bound, and dual SDDP for deterministic upper bounds. In this paper, we leverage the dual SDDP algorithm to compute a policy with guaranteed risk-adjusted performance for multistage stochastic linear problems.

Suggested Citation

  • Lucas Merabet & Bernardo Freitas Paulo Costa & Vincent Leclere, 2024. "Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems," Computational Management Science, Springer, vol. 21(2), pages 1-25, December.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:2:d:10.1007_s10287-024-00524-z
    DOI: 10.1007/s10287-024-00524-z
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    References listed on IDEAS

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    1. Shapiro, Alexander & Tekaya, Wajdi & da Costa, Joari Paulo & Soares, Murilo Pereira, 2013. "Risk neutral and risk averse Stochastic Dual Dynamic Programming method," European Journal of Operational Research, Elsevier, vol. 224(2), pages 375-391.
    2. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    3. Guigues, Vincent & Shapiro, Alexander & Cheng, Yi, 2023. "Duality and sensitivity analysis of multistage linear stochastic programs," European Journal of Operational Research, Elsevier, vol. 308(2), pages 752-767.
    4. Andy Philpott & Vitor de Matos & Erlon Finardi, 2013. "On Solving Multistage Stochastic Programs with Coherent Risk Measures," Operations Research, INFORMS, vol. 61(4), pages 957-970, August.
    5. 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.
    6. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    7. P. Girardeau & V. Leclere & A. B. Philpott, 2015. "On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 130-145, February.
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