Paper: arXiv 2603.24349
Authors: Marcelo Righi, Rodrigo Targino
Abstract
We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the baseline risk measure. We prove continuity in the neighborhood radius and provide a stable large-radius behavior. In Banach lattices, the approach leads to a convex risk measure and under separability of the space, a dual representation through a penalty term based on an inf-convolution taken over a Gelfand integral constraint. We also relate our veraging to aggregation at the distribution and quantile levels of payoffs, obtaining dominance and coincidence results. Numerical illustrations are conducted to verify calibration and sensitivity.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 3.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper introduces an innovative theoretical framework for robust risk measurement by averaging over payoff uncertainty neighborhoods using advanced functional analysis (Banach lattices, Gelfand integration, inf-convolutions). However, it relies primarily on abstract mathematical proofs and toy numerical illustrations rather than rigorous empirical backtesting with real market datasets.
Research Flowchart
flowchart TD
A["Research Goal: Robust Risk Measurement<br/>under Payoff Uncertainty"] --> B["Input: Baseline Risk Measure &<br/>Metric-Weighted Nearby Payoffs"]
B --> C["Averaging Approach Construction:<br/>Weighting & Averaging Over Neighborhood"]
C --> D["Theoretical Analysis in Banach Lattices:<br/>Convexity, Continuity & Inf-Convolution Dual"]
C --> E["Aggregation Analysis:<br/>Distribution & Quantile Level Relations"]
D --> F["Numerical Testing:<br/>Calibration & Sensitivity Verification"]
E --> F
F --> G["Key Outcomes: Continuous/Stable Robust Measure<br/>with Convexity & Duality Guarantees"]