Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping

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.