Model Aggregation for Risk Evaluation and Robust Optimization

TL;DR

This paper introduces the model aggregation (MA) approach for risk evaluation and robust optimization, providing explicit formulas and axiomatic characterizations that improve upon traditional worst-case methods in finance and portfolio management.

Contribution

The paper presents a novel MA approach that offers explicit formulas, convex reformulations, and new axiomatic characterizations for risk measures, advancing robust risk evaluation methods.

Findings

MA produces both robust risk values and distributional models.

Explicit formulas are derived for Wasserstein and mean-variance sets.

New axiomatic characterizations for VaR and ES are established.

Abstract

We introduce a new approach for prudent risk evaluation based on stochastic dominance, which will be called the model aggregation (MA) approach. In contrast to the classic worst-case risk (WR) approach, the MA approach produces not only a robust value of risk evaluation but also a robust distributional model, independent of any specific risk measure. The MA risk evaluation can be computed through explicit formulas in the lattice theory of stochastic dominance, and under some standard assumptions, the MA robust optimization admits a convex-program reformulation. The MA approach for Wasserstein and mean-variance uncertainty sets admits explicit formulas for the obtained robust models. Via an equivalence property between the MA and the WR approaches, new axiomatic characterizations are obtained for the Value-at-Risk (VaR) and the Expected Shortfall (ES, also known as CVaR). The new approach is illustrated with various risk measures and examples from portfolio optimization.