Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping

Alois Pichler, Rui Peng Liu () and Alexander Shapiro ()
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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

Operations Research, 2022, vol. 70, issue 4, 2439-2455

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.

Keywords: Optimization; stochastic programming; coherent risk measures; time consistency; dynamic equations; optimal stopping time; Snell envelope; inventory model; American put option (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:4:p:2439-2455

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