Paper: arXiv 2610.17481

Authors: Pedro Cadahia

Abstract

Estimation error in short, correlated pricing panels is dominated by trajectory dispersion rather than sampling noise, creating an identification shortfall that only independently assigned variation can resolve. We propose a guided iteration methodology to decide how much variation to generate, where, and for how long: a cyclic price-perturbation scheme under a revenue-at-risk budget, framed as variance minimization over design-specific error covariances, analogous to portfolio selection. We establish four key results: (1) a closed-form minimum-variance combination rule; (2) proof that a convex cost of intensity yields an interior, spread-out allocation, whereas under a concave tolerable-volume-loss cost, concentrating intensity into fewer perturbations pays off only with heterogeneous candidates, priced-in fixed costs, or perturbations beyond the cost curve’s inflection point; (3) a discounted recursion yielding a data-dependent exit timeline from the experimentation zone; and (4) an application to Dominick’s retail data, in which about five designed independent units match the precision of approximately 700 passive equivalents in the anchor category, while a fast proxy across ten categories achieves a median 97% variance reduction relative to passive panels. Sixteen comparisons (eleven pre-specified) support the theory: greedy selection achieves 90-93% of the global optimum across more than fifty exhaustively verifiable instances, and the recursion reaches its predicted 90%-of-steady-state benchmark two cycles early, though a parametric bootstrap indicates that its delta-method interval understates the right-tail risk. Boundary conditions show that regularized covariance estimators extend plug-in noise tolerance from 29% to beyond 50%, submodularity holds up to a clear curvature threshold, and a shared shock imposes a fundamental precision floor.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical and novel methodology for optimizing price experiments, grounded in portfolio theory. It demonstrates strong empirical rigor through application to real-world retail data and extensive validation, making it a significant contribution to quantitative finance. The detailed results and boundary conditions further enhance its completeness.

Research Flowchart

  flowchart TD
    A[Research Goal: Resolve Identification Shortfall in Short, Correlated Pricing Panels] --> B{Guided Iteration Methodology: Variance Minimization under Revenue-at-Risk Budget};
    B --> C{Computational Processes: Closed-form Min-Variance Rule, Discounted Recursion, Greedy Selection};
    C --> D[Data/Inputs: Dominick's Retail Data, Experimentation Parameters];
    D --> E[Key Findings/Outcomes: 5 Designed Units ~ 700 Passive Equivalents, 97% Variance Reduction, Theory Support & Boundary Conditions];