Convex Order Beyond Dimension One: Projection Tests, Counterexamples and Gaussian Mixtures

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Highly relevant for risk management, stop-loss order comparisons, and understanding the limitations of comparing portfolio risks via linear projections. Directly applicable to comparing Gaussian-distributed asset returns or risk factors.

Theoretical paper. Implementation involves checking matrix inequalities (e.g., Σ1 ≤ Σ) for Gaussian comparisons, which is computationally simple, but the underlying theory is complex.

The paper provides complete mathematical proofs, definitions, and explicit counterexamples. No external data or code is required to verify the theoretical results.