Model Aggregation for Risk Evaluation and Robust Optimization

We introduce a new approach for prudent risk evaluation based on stochastic dominance, and it is 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 WR approaches, new axiomatic characterizations are obtained for the value at risk and the expected shortfall (also known as conditional value at risk). The new approach is illustrated with various risk measures and examples from portfolio optimization.