Model Monitoring: A General Framework with an Application to Non-life Insurance Pricing

ArXiv ID: 2510.04556 “View on arXiv”

Authors: Alexej Brauer, Paul Menzel, Mario V. Wüthrich

Abstract

Maintaining the predictive performance of pricing models is challenging when insurance portfolios and data-generating mechanisms evolve over time. Focusing on non-life insurance, we adopt the concept-drift terminology from machine learning and distinguish virtual drift from real concept drift in an actuarial setting. Methodologically, we (i) formalize deviance loss and Murphy’s score decomposition to assess global and local auto-calibration; (ii) study the Gini score as a rank-based performance measure, derive its asymptotic distribution, and develop a consistent bootstrap estimator of its asymptotic variance; and (iii) combine these results into a statistically grounded, model-agnostic monitoring framework that integrates a Gini-based ranking drift test with global and local auto-calibration tests. An application to a modified motor insurance portfolio with controlled concept-drift scenarios illustrates how the framework guides decisions on refitting or recalibrating pricing models.

Keywords: Concept drift, Actuarial pricing, Gini score, Auto-calibration, Model monitoring, Insurance

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper presents a statistically grounded framework with advanced derivations, such as the asymptotic distribution of the Gini score and Murphy’s decomposition, indicating high mathematical density. It demonstrates empirical applicability through a controlled concept-drift simulation on a modified motor insurance portfolio, showing data-heavy implementation and backtest-ready guidance.

  flowchart TD
    A["Research Goal<br>Monitor Pricing Model Performance under<br>Concept Drift in Non-Life Insurance"] --> B["Methodology Development"]
    
    subgraph B ["Key Methodology Steps"]
        B1["Formalize Deviance Loss<br>Murphy Score Decomposition<br>Global & Local Auto-calibration"]
        B2["Analyze Gini Score<br>Asymptotic Distribution<br>Bootstrap Variance Estimator"]
        B3["Integrate Framework<br>Gini Ranking Drift Test +<br>Auto-calibration Tests"]
    end
    
    B --> C["Data & Inputs<br>Motor Insurance Portfolio<br>Simulated Concept Drift Scenarios"]
    
    C --> D["Computational Processes<br>Statistical Tests + Model-Agnostic<br>Drift Detection"]
    
    D --> E["Key Findings & Outcomes<br>1. Distinguished Virtual vs Real Drift<br>2. Consistent Bootstrap Estimator<br>3. Framework for Refit/Recalibration Decisions"]