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Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping

Author

Listed:
  • Alois Pichler

    (Fakultät für Mathematik, Technische Universität Chemnitz, D–09111 Chemnitz, Germany)

  • Rui Peng Liu

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Alexander Shapiro

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

This paper addresses time consistency of risk-averse optimal stopping in stochastic optimization. It is demonstrated that time-consistent optimal stopping entails a specific structure of the functionals describing the transition between consecutive stages. The stopping risk measures capture this structural behavior and allow natural dynamic equations for risk-averse decision making over time. Consequently, associated optimal policies satisfy Bellman’s principle of optimality, which characterizes optimal policies for optimization by stating that a decision maker should not reconsider previous decisions retrospectively. We also discuss numerical approaches to solving such problems.

Suggested Citation

  • Alois Pichler & Rui Peng Liu & Alexander Shapiro, 2022. "Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping," Operations Research, INFORMS, vol. 70(4), pages 2439-2455, July.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:4:p:2439-2455
    DOI: 10.1287/opre.2021.2120
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