Decomposability and time consistency of risk averse multistage programs

TL;DR

This paper explores the relationship between two approaches to ensuring time consistency in risk-averse multistage stochastic optimization, focusing on decomposability and conditional optimality.

Contribution

It establishes a connection between the properties of risk measures and the conditional optimality of solutions in multistage programs.

Findings

Identifies conditions under which risk measures are decomposable.

Shows how decomposability relates to conditional optimality.

Provides theoretical insights into time consistency in risk-averse optimization.

Abstract

Two approaches to time consistency of risk averse multistage stochastic problems were discussed in the recent literature. In one approach certain properties of the cor-responding risk measure are postulated which imply its decomposability. The other approach deals directly with conditional optimality of solutions of the considered problem. The aim of this paper is to discuss a relation between these two approaches.