Orlicz-Lorentz premia and distortion Haezendonck-Goovaerts risk measures

Paper: arXiv 2512.03267

Authors: Aline Goulard, Karl Grosse-Erdmann

Abstract

In financial and actuarial research, distortion and Haezendonck-Goovaerts risk measures are attractive due to their strong properties. They have so far been treated separately. In this paper, following a suggestion by Goovaerts, Linders, Van Weert, and Tank, we introduce and study a new class of risk measure that encompasses the distortion and Haezendonck-Goovaerts risk measures, aptly called the distortion Haezendonck-Goovaerts risk measures. They will be defined on a larger space than the space of bounded risks. We provide situations where these new risk measures are coherent, and explore their risk theoretic properties.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework that unifies distortion and Haezendonck-Goovaerts risk measures using Orlicz-Lorentz spaces. While mathematically dense, complete with formal proofs and analysis of domains and Fatou properties, it is purely theoretical and lacks empirical backtesting or real-world financial data applications.

Research Flowchart

  flowchart TD
    A[Research Goal: Unify Distortion & Haezendonck-Goovaerts Risk Measures] --> B[Input: Financial Risks beyond Bounded Space & Young Functions]
    B --> C[Methodology: Construct Distortion Haezendonck-Goovaerts Risk Measures via Orlicz-Lorentz Premia]
    C --> D[Computational Analysis: Evaluate Axiomatic Risk-Theoretic Properties]
    D --> E[Key Finding: Establish Conditions for Coherence & Expanded Application Domains]