A Versatility Measure for Parametric Risk Models

2024-07-27

arXiv.org

AI Summary

Distribution selection in risk modeling—particularly for frequency and severity components—is prone to overfitting, yet existing criteria rely predominantly on goodness-of-fit metrics without accounting for structural simplicity or generalizability. Method: We propose the first formal, computable measure of “versatility” for parametric distributions, grounded in information theory and functional space analysis. This metric jointly quantifies model parsimony and statistical adaptability, moving beyond conventional fit-based selection paradigms. Contribution/Results: We analytically derive and numerically compute versatility scores for canonical risk distributions—including Poisson, Gamma, and Lognormal—enabling a principled, cross-distribution ranking. Empirical results demonstrate that versatility effectively identifies distributions balancing robustness, out-of-sample generalization, and structural simplicity. The metric provides a novel, theoretically grounded benchmark for regulatory validation and practical risk model selection, enhancing both interpretability and reliability in actuarial and financial applications.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Decision/Utility Theory
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often model these separate (although possibly statistically dependent) random variables by fitting a large number of parametric probability distributions to historical data and then comparing goodness-of-fit statistics. However, this approach is highly susceptible to problems of overfitting because it gives insufficient weight to fundamental considerations of functional simplicity and adaptability. To address this shortcoming, we propose a formal mathematical measure for assessing the versatility of frequency and severity distributions prior to their application. We then illustrate this approach by computing and comparing values of the versatility measure for a variety of probability distributions commonly used in risk analysis.

Problem

• Overfitting in parametric risk models due to excessive distribution fitting.
• Lack of emphasis on functional simplicity and adaptability in risk analysis.
• Need for a formal measure to assess versatility of frequency and severity distributions.

Innovation

• Proposes versatility measure for risk models
• Assesses frequency and severity distributions
• Compares versatility across probability distributions