Risk averse stochastic programming: time consistency and optimal stopping

TL;DR

This paper explores the concept of time consistency in risk-averse stochastic programming, analyzing how recursive risk measures and stopping times influence decision-making over time.

Contribution

It introduces the framework of stopping time risk measures and examines the conflict between time consistency and classical risk measure properties.

Findings

Time consistency can conflict with classical risk measure properties.

Stopping time risk measures are introduced to address dynamic decision-making.

The paper provides a general formulation of time consistent stochastic optimization.

Abstract

Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically or time consistent and introduces stopping time risk measures. It turns out that the paradigm of time consistency is in conflict with various desirable, classical properties of general risk measures.