Robust risk measures: an averaging approach

Battle Count: 97

The paper addresses fundamental risk measurement under model uncertainty, which is directly relevant to quantitative trading risk management. The averaging approach provides a less conservative alternative to worst-case robust risk measures, which could improve capital allocation and position sizing. The Wasserstein metric framework and Bayesian interpretation are relevant for model uncertainty in trading strategies. However, the paper is primarily theoretical and does not provide direct trading signals or strategy implementations. The numerical examples (Gaussian families, Expected Shortfall) are relevant to portfolio risk assessment.

High complexity due to: (1) Requires understanding of Banach lattice theory, convex analysis, and Gelfand integration; (2) The dual representation involves inf-convolution over measurable selections with integral constraints; (3) Numerical implementation requires Monte Carlo methods in potentially infinite-dimensional spaces; (4) The Wasserstein metric computations and Normal-Gamma prior sampling add practical complexity; (5) The curse of dimensionality in infinite-dimensional settings makes direct computation infeasible, requiring finite-dimensional approximations.

The paper is primarily theoretical with proofs. Numerical illustrations (Section 5) use Monte Carlo simulations with specified parameters (N=10^6 draws, specific Normal-Gamma prior parameters, Wasserstein metric settings). However, no code repository or supplementary materials are mentioned. The theoretical framework is fully specified mathematically, but reproducing the numerical experiments would require implementing the Monte Carlo procedures described in Examples 8-10.