Varying risk exposure in auto insurance: a weighted tweedie framework for experience rating an cancellation penalties

TL;DR

This paper introduces a Tweedie-based model for auto insurance that accounts for policy cancellations and exposure variations, improving risk assessment and pricing strategies.

Contribution

It develops a novel weighted Tweedie framework with penalty structures dependent on exposure, enhancing experience rating accuracy in the presence of cancellations.

Findings

The model captures differences in claims between policyholders who cancel and those who do not.

Empirical results show improved model fit using deviance and Lorenz curve criteria.

The approach enables insurers to incorporate cancellation penalties for better risk management.

Abstract

This paper proposes a new family of Tweedie-based ratemaking models that explicitly account for mid-term policy cancellations. Using an automobile insurance dataset from a Canadian insurer, we document a marked difference in claims experience between policyholders who maintain their coverage until maturity and those who cancel their policies mid-term. Building on the classical Tweedie framework, we introduce flexible weighting functions and a premium penalty structure that depend on the level of exposure, allowing for a more realistic representation of the earned premium when coverage is interrupted before the end of the policy period. We compare several weighting structures within the Tweedie framework and examine their theoretical properties, as well as their empirical performance using deviance-based model comparison criteria, an area-between-curves criterion derived from concentration and Lorenz curves, and Murphy diagrams grounded in Bregman dominance. To operationalize the proposed models, monotonicity and non-negativity constraints are imposed on the penalty function, ensuring consistency with actuarial principles. Finally, using real-world data, we show that this approach provides both a strategic and competitive advantage: it allows the insurer to indirectly compensate for large losses through a cancellation surcharge, while preserving actuarial coherence and statistical consistency.