Robust quasi-convex risk measures and applications

Battle Count: 65

The paper provides a rigorous theoretical foundation for risk measurement under model ambiguity, which is directly relevant to quantitative trading risk management. The robustification framework can inform capital allocation decisions, stress testing, and portfolio risk assessment. However, the paper is purely theoretical with no trading strategies, backtests, or empirical results. Its relevance is at the level of risk framework design rather than direct trading signal generation. The Wasserstein-based uncertainty sets and capital allocation results have practical implications for risk managers in trading desks.

The paper is highly theoretical, requiring advanced knowledge of functional analysis, convex analysis, measure theory, and mathematical finance. Implementing the framework would require: (1) constructing appropriate uncertainty sets in Lp spaces, (2) computing dual representations involving penalty-type functionals over probability measures, (3) handling quasi-convexity and c-quasi-convexity conditions on set-valued maps, (4) solving optimization problems involving support functions. No code or algorithms are provided. The mathematical sophistication is very high, targeting researchers in mathematical finance rather than practitioners.

This is a purely theoretical paper with complete mathematical proofs. All definitions, propositions, lemmas, and theorems are fully stated and proved within the paper. Reproducibility depends on verifying the mathematical proofs, which are self-contained. No computational experiments or code are involved. The paper builds on well-established prior work (Cerreia-Vioglio et al. 2011, Frittelli and Maggis 2011, Righi 2024, Moresco et al. 2025) with clear references.