A portfolio-anchored frequency–severity behavioral risk index for trip and driver assessment using telematics signals

In this paper, we propose a frequency–severity joint trip-level behavioral risk index that combines the frequency of driving patterns with a signal severity component reflecting how extreme such patterns are relative to a portfolio-level baseline. The severity is quantified through an inverse-probability penalty that increases with the extremeness/rarity of tail observations, not claim size. For high-frequency telematics data, we construct a multi-scale representation using the Maximal Overlap Discrete Wavelet Transform (MODWT), which preserves driving patterns across multiple time scales. To capture severity as tail extremeness/rarity, we model the portfolio distribution using a Gaussian–Uniform mixture with a layered tail structure, where Gaussian components describe typical driving patterns, and the tail is partitioned into ordered severity layers that reflect increasing extremeness. We develop a likelihood-based estimation procedure that makes inference feasible for this mixture model. The estimated severity layers are used to construct multi-layer tail counts (MLTCs) at the trip level, which are modeled within a Poisson–Gamma framework to yield a closed-form posterior risk index that jointly reflects frequency and severity. This conjugate structure supports sequential updating, enabling the construction of evolving driver-level risk profiles. Using the UAH-DriveSet controlled dataset, we demonstrate that the proposed index separates instructed behavioral states, such as normal , aggressive , and drowsy , and identifies high-risk trips. The proposed model improves binary classification of normal versus risky trips, with sensitivity analyses showing that its performance is stable with respect to the choices of hyperparameters, including the severity weighting function, frequency distribution, and the data thinning phase.