Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping

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.

Automated summary

This paper discusses the time consistency of risk-averse optimal stopping in stochastic optimization, demonstrating the importance of specific structures and risk measures in decision-making processes. The discussion also highlights the significance of Bellman's principle of optimality in characterizing optimal policies for such problems.