Orlicz-Lorentz Premia and Distortion Haezendonck-Goovaerts Risk Measures

Battle Count: 75

The paper is highly relevant to quantitative finance and risk management. Coherent risk measures are fundamental to portfolio risk assessment, regulatory capital calculations, and trading risk limits. The distortion Haezendonck-Goovaerts risk measures generalize both distortion risk measures (including VaR, TVaR/Expected Shortfall) and Haezendonck-Goovaerts measures, providing a unified framework. However, the paper is purely theoretical with no direct trading strategy applications, backtesting, or empirical validation. The practical implementation would require significant additional work in numerical methods and calibration.

Extremely high complexity. The paper requires deep knowledge of functional analysis (Orlicz spaces, Lorentz spaces, Orlicz-Lorentz spaces), measure theory (Lebesgue-Stieltjes integrals, quantile functions), convex analysis, and risk theory. The definitions involve infima over function spaces, the proofs use sophisticated techniques (dominated convergence, monotone convergence, Jensen's inequality, comonotonicity arguments, stop-loss order). Practical implementation would require solving optimization problems involving integrals of Young functions with respect to distortion measures, and determining natural domains of definition. No code or algorithms are provided.

This is a pure mathematics paper with complete formal proofs. All definitions, theorems, propositions, and lemmas are stated rigorously with full proofs provided. The mathematical arguments are self-contained and verifiable. No computational experiments or data are involved. The paper builds on well-established literature in Orlicz spaces, Lorentz spaces, and risk measure theory.