Spectral Risk Measures, With Adaptions For Stochastic Optimization

TL;DR

This paper develops efficient evaluation schemes for spectral risk measures, enabling their integration into stochastic optimization problems and improving risk quantification in decision-making models.

Contribution

It introduces new representations of spectral risk measures tailored for stochastic optimization, facilitating concise formulations and efficient algorithms.

Findings

New representations of spectral risk measures for optimization

Concise problem formulations for risk-aware stochastic optimization

Algorithms enabling spectral risk measures in stochastic optimization

Abstract

Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. For this purpose it is important to have an adjusted, adapted and efficient evaluation scheme for the risk measure available. In this article different representations of an important class of risk measures, the spectral risk measures, are elaborated. The results allow concise problem formulations, they are particularly adapted for stochastic optimization problems. Efficient evaluation algorithms can be built on these new results, which finally make optimization problems involving spectral risk measures eligible for stochastic optimization.