Frequency–Severity Dependence Diagnostics in Motor Casco Insurance: From Measurement Bias to Risk-Based Premium Pricing and Claims Reserving Strategies
- 1Department of Statistics, Yıldız Technical University, 34220 Istanbul, Türkiye
- 2Actuarial Department, Türk Reasürans, 34782 Istanbul, Türkiye
Abstract
Diagnostics for frequency–severity dependence in insurance can indicate a positive association even when claim counts and claim sizes are independent, because the association is generated by how the claims are summarized rather than by the claims process. We study the association between a policy’s claim count and its average claim size, which arises by construction, give its mechanism on the rank scale, and decompose it in a Turkish motor casco portfolio of 818,789 policies and 214,283 claims: the observed count–average Kendall’s τ of +0.08 is reproduced in full by permuting severities across claims (+0.11 under exact independence), so that a copula fitted to this pair would absorb an association that does not belong to the loss process. We then propose a leakage-safe diagnostic protocol that combines claim-level rank measures, covariate-adjusted regression, cluster-robust inference with a power analysis, an equivalence test, and a replicated synthetic positive control. Clean measurement leaves a small negative association (τ = −0.0065) whose effect on a Solvency-II-style capital proxy cannot be distinguished from zero, whereas injected dependence is reliably detected. In the decision layer, modeling the pure premium rather than frequency alone drives risk differentiation, a trend-based on-level adjustment restores the premium level, and the paid, incurred, and case-reserve bases of the book are reconciled before a reserve confidence level is chosen. The practical message is that measurement should precede model complexity: a dependence layer is warranted only after it survives artifact-safe measurement.
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BibTeX
@article{arslan2026frequencyseverity,
title = {{Frequency–Severity Dependence Diagnostics in Motor Casco Insurance: From Measurement Bias to Risk-Based Premium Pricing and Claims Reserving Strategies}},
author = {Yusuf Arslan and Filiz Karaman},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14214104},
url = {https://www.mdpi.com/2227-7390/14/21/4104},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Frequency–Severity Dependence Diagnostics in Motor Casco Insurance: From Measurement Bias to Risk-Based Premium Pricing and Claims Reserving Strategies
AU - Yusuf Arslan
AU - Filiz Karaman
PY - 2026
DA - 2026/11/09
JO - Mathematics
DO - 10.3390/math14214104
UR - https://www.mdpi.com/2227-7390/14/21/4104
AB - Diagnostics for frequency–severity dependence in insurance can indicate a positive association even when claim counts and claim sizes are independent, because the association is generated by how the claims are summarized rather than by the claims process. We study the association between a policy’s claim count and its average claim size, which arises by construction, give its mechanism on the rank scale, and decompose it in a Turkish motor casco portfolio of 818,789 policies and 214,283 claims: the observed count–average Kendall’s τ of +0.08 is reproduced in full by permuting severities across claims (+0.11 under exact independence), so that a copula fitted to this pair would absorb an association that does not belong to the loss process. We then propose a leakage-safe diagnostic protocol that combines claim-level rank measures, covariate-adjusted regression, cluster-robust inference with a power analysis, an equivalence test, and a replicated synthetic positive control. Clean measurement leaves a small negative association (τ = −0.0065) whose effect on a Solvency-II-style capital proxy cannot be distinguished from zero, whereas injected dependence is reliably detected. In the decision layer, modeling the pure premium rather than frequency alone drives risk differentiation, a trend-based on-level adjustment restores the premium level, and the paid, incurred, and case-reserve bases of the book are reconciled before a reserve confidence level is chosen. The practical message is that measurement should precede model complexity: a dependence layer is warranted only after it survives artifact-safe measurement.
SN - 2227-7390
ER -